4505:
1151:
1544:
3912:
174:
3695:
606:
3785:
390:
502:
2370:
1805:
1457:
1026:
909:
862:
543:
96:
1738:
1705:
1665:
1601:
966:
818:
747:
657:
472:
296:
242:
3822:
1257:
437:
4394:
4019:
3073:
2290:
3861:
3629:
2335:
1954:
is not in general a Banach space with respect to the uniform norm since it may contain unbounded functions. Hence it is more typical to consider the space, denoted here
3988:
2128:
2455:
2416:
2206:
1292:
2082:
1988:
351:
2264:
1564:
1500:
1417:
2235:
2157:
1952:
1900:
1840:
1350:
1321:
2011:
1923:
1863:
1480:
687:
209:
4057:
4014:
2042:
1758:
1625:
1390:
1370:
1195:
1175:
1093:
1073:
1046:
990:
929:
785:
714:
567:
492:
319:
52:
4220:
3128:
4347:
4202:
3100:
4539:
4178:
2739:
2734:
2566:
3447:
3389:
2505:
2497:
3288:
2727:
2755:
4070:
4159:
4050:
2929:
2712:
2535:
4429:
2847:
2690:
109:
3158:
4074:
3377:
3313:
2864:
1098:
3372:
3051:
2830:
3143:
872:
4225:
3410:
3188:
3133:
4281:
2966:
764:
4544:
4508:
4230:
4215:
4043:
3245:
3235:
3195:
3163:
3090:
2635:
1505:
4245:
3173:
4554:
3583:
2559:
4490:
4250:
3942:
3744:
3113:
3108:
2793:
1810:
3877:
4444:
4368:
3406:
3220:
3205:
3003:
2976:
2941:
2686:
623:
4485:
3700:
3350:
3168:
4534:
4301:
3394:
3367:
3013:
2682:
4235:
3917:
3210:
3200:
3118:
102:
with respect to the pointwise addition of functions and scalar multiplication by constants. It is, moreover, a
4337:
4138:
3651:
3056:
2983:
2937:
2852:
2677:
2013:
This is a Banach space (in fact a commutative Banach algebra with identity) with respect to the uniform norm. (
4210:
3183:
3123:
576:
3748:
4434:
356:
4549:
4529:
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3225:
3138:
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4009:
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831:
512:
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65:
17:
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444:
268:
214:
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3153:
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2649:
2496:. International Series in Pure and Applied Mathematics. Vol. 8 (Second ed.). New York, NY:
1200:
25:
395:
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1049:
185:
21:
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4306:
4024:
3935:
3839:
3602:
3573:
3569:
3558:
3528:
3524:
3345:
3303:
2910:
2820:
2765:
2612:
2374:
2295:
969:
821:
3951:
2094:
262:
2421:
2385:
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1262:
4419:
3705:
3178:
2959:
2902:
2882:
2531:
2511:
2501:
2051:
2048:
Hausdorff space. In this case, it is possible to identify a pair of distinguished subsets of
1957:
1604:
324:
2240:
1549:
1485:
1402:
494:
is an infinite space (since it separates points). Hence, in particular, it is generally not
4424:
4342:
4311:
4291:
4276:
4271:
4266:
4103:
3335:
3330:
3318:
3230:
3215:
3078:
3018:
2993:
2924:
2914:
2777:
2722:
1567:
4286:
4240:
4188:
4183:
4154:
4035:
3355:
3340:
3266:
3240:
3068:
3061:
3028:
2988:
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2874:
2842:
2707:
2639:
2211:
2160:
2133:
2045:
1928:
1876:
1816:
1671:
1326:
1297:
1028:
In the case of complex functions, the statement holds with the additional hypothesis that
750:
660:
609:
495:
59:
32:
4113:
1993:
1905:
1845:
1462:
669:
191:
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3873:
3790:
3533:
3399:
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2655:
2607:
2027:
2021:
1902:
of real or complex-valued continuous functions can be defined on any topological space
1768:
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1743:
1610:
1375:
1355:
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1031:
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914:
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477:
304:
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245:
37:
4523:
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4404:
4133:
4118:
4108:
3930:
3736:
3543:
3497:
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3283:
3278:
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2892:
2825:
2798:
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2590:
2491:
1668:
1420:
1393:
754:
663:
570:
546:
29:
4470:
4123:
4093:
3442:
3437:
2897:
2887:
2760:
2750:
2595:
2575:
2523:
2487:
1154:
177:
103:
99:
55:
2024:, to further refine this general definition by considering the special case when
4399:
4389:
4296:
4098:
3731:
3647:
3553:
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2515:
1813:
implies that any normed space is isometrically isomorphic to a subspace of
3866:
3829:
3713:
3639:
3599:
3502:
3325:
613:
181:
3634:
3468: ((cs, lcs)-closed, (cs, bcs)-complete, (lower) ideally convex, (H
2717:
932:
2544:
1459:
Then there is a one-to-one correspondence between Δ and the points of
1502:
can be identified with the collection of all complex homomorphisms
4039:
2548:
612:
of a measure, is also a Banach space belonging to the class of
2353:
1780:
1716:
1683:
1643:
1579:
1511:
1432:
1129:
1110:
1001:
944:
884:
837:
796:
725:
635:
518:
450:
368:
274:
220:
71:
968:
that contains all constants and separates points, then the
1157:
of algebras which commutes with complex conjugation, then
689:
by a different form of the Riesz representation theorem. (
1146:{\displaystyle F:{\mathcal {C}}(X)\to {\mathcal {C}}(Y)}
3954:
3880:
3842:
3803:
3751:
3654:
3605:
2424:
2388:
2343:
2298:
2272:
2243:
2214:
2175:
2136:
2097:
2054:
2030:
1996:
1960:
1931:
1908:
1879:
1848:
1819:
1777:
1746:
1713:
1680:
1640:
1613:
1576:
1552:
1508:
1488:
1465:
1429:
1405:
1378:
1358:
1329:
1300:
1265:
1203:
1183:
1163:
1101:
1081:
1061:
1034:
998:
978:
941:
917:
881:
834:
793:
773:
722:
702:
672:
632:
579:
555:
515:
480:
447:
398:
359:
327:
307:
271:
217:
194:
112:
68:
40:
4458:
4382:
4361:
4320:
4259:
4201:
4147:
4082:
3997:
3582:
3511:
3420:
3254:
3099:
3027:
2873:
2786:
2700:
2583:
1627:
is homeomorphic to Δ equipped with this topology. (
4395:Spectral theory of ordinary differential equations
3982:
3906:
3855:
3816:
3779:
3689:
3623:
2449:
2410:
2364:
2329:
2284:
2258:
2229:
2200:
2151:
2122:
2076:
2036:
2005:
1982:
1946:
1917:
1894:
1857:
1834:
1799:
1752:
1732:
1699:
1659:
1619:
1595:
1558:
1539:{\displaystyle {\mathcal {C}}(X)\to \mathbb {C} .}
1538:
1494:
1474:
1451:
1411:
1384:
1364:
1344:
1315:
1286:
1251:
1189:
1169:
1145:
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1067:
1040:
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984:
960:
923:
903:
856:
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741:
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681:
651:
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537:
486:
466:
431:
384:
345:
313:
290:
236:
203:
168:
90:
46:
126:
2085:
2014:
617:
24:, a fundamental role is played by the space of
3907:{\displaystyle S\left(\mathbb {R} ^{n}\right)}
545:Specifically, this dual space is the space of
4051:
4015:Mathematical formulation of quantum mechanics
2560:
2457:In particular, the latter is a Banach space.
8:
2237:consisting of functions such that for every
1674:if and only if it is (uniformly) bounded in
503:Riesz–Markov–Kakutani representation theorem
119:
113:
2020:It is sometimes desirable, particularly in
169:{\displaystyle \|f\|=\sup _{x\in X}|f(x)|,}
4086:
4058:
4044:
4036:
2567:
2553:
2545:
1707:and pointwise convergent. In particular,
3971:
3953:
3894:
3890:
3889:
3879:
3847:
3841:
3808:
3802:
3756:
3750:
3690:{\displaystyle B_{p,q}^{s}(\mathbb {R} )}
3680:
3679:
3670:
3659:
3653:
3604:
2429:
2423:
2393:
2387:
2342:
2316:
2299:
2297:
2271:
2242:
2213:
2180:
2174:
2163:. This is called the space of functions
2135:
2102:
2096:
2059:
2053:
2029:
1995:
1965:
1959:
1930:
1907:
1878:
1847:
1818:
1779:
1778:
1776:
1745:
1715:
1714:
1712:
1682:
1681:
1679:
1642:
1641:
1639:
1612:
1578:
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1575:
1551:
1529:
1528:
1510:
1509:
1507:
1487:
1464:
1431:
1430:
1428:
1404:
1377:
1357:
1328:
1299:
1264:
1202:
1182:
1162:
1128:
1127:
1109:
1108:
1100:
1080:
1060:
1033:
1000:
999:
997:
977:
943:
942:
940:
916:
883:
882:
880:
836:
835:
833:
795:
794:
792:
772:
724:
723:
721:
701:
671:
634:
633:
631:
578:
554:
517:
516:
514:
479:
449:
448:
446:
397:
367:
366:
358:
326:
306:
273:
272:
270:
219:
218:
216:
193:
158:
141:
129:
111:
70:
69:
67:
39:
4348:Group algebra of a locally compact group
601:{\displaystyle \operatorname {rca} (X).}
3780:{\displaystyle L^{\lambda ,p}(\Omega )}
2477:Hewitt, Edwin; Stromberg, Karl (1965),
2165:vanishing in a neighborhood of infinity
608:This space, with the norm given by the
4020:Ordinary Differential Equations (ODEs)
3134:Banach–Steinhaus (Uniform boundedness)
2372:This is called the space of functions
1095:are two compact Hausdorff spaces, and
385:{\displaystyle f\in {\mathcal {C}}(X)}
353:are distinct points, then there is an
1628:
690:
249:
7:
2498:McGraw-Hill Science/Engineering/Math
2467:Dunford, N.; Schwartz, J.T. (1958),
2365:{\displaystyle x\in X\backslash K.}
1990:of bounded continuous functions on
3848:
3809:
3771:
3615:
1925:In the non-compact case, however,
1800:{\displaystyle {\mathcal {C}}(X).}
1570:with respect to this pairing with
1553:
1489:
1452:{\displaystyle {\mathcal {C}}(X).}
1406:
1021:{\displaystyle {\mathcal {C}}(X).}
911:In the case of real functions, if
904:{\displaystyle {\mathcal {C}}(X).}
857:{\displaystyle {\mathcal {C}}(X),}
538:{\displaystyle {\mathcal {C}}(X).}
91:{\displaystyle {\mathcal {C}}(X),}
14:
3512:Subsets / set operations
3289:Differentiation in Fréchet spaces
1733:{\displaystyle {\mathcal {C}}(X)}
1700:{\displaystyle {\mathcal {C}}(X)}
1660:{\displaystyle {\mathcal {C}}(X)}
1596:{\displaystyle {\mathcal {C}}(X)}
1352:are isomorphic as algebras, then
961:{\displaystyle {\mathcal {C}}(X)}
813:{\displaystyle {\mathcal {C}}(X)}
742:{\displaystyle {\mathcal {C}}(X)}
652:{\displaystyle {\mathcal {C}}(X)}
474:is infinite-dimensional whenever
467:{\displaystyle {\mathcal {C}}(X)}
291:{\displaystyle {\mathcal {C}}(X)}
237:{\displaystyle {\mathcal {C}}(X)}
4504:
4503:
4430:Topological quantum field theory
505:gives a characterization of the
180:. The uniform norm defines the
3817:{\displaystyle \ell ^{\infty }}
1252:{\displaystyle F(h)(y)=h(f(y))}
4540:Theory of continuous functions
3977:
3958:
3774:
3768:
3684:
3676:
3618:
3612:
3206:Lomonosov's invariant subspace
3129:Banach–Schauder (open mapping)
2441:
2435:
2405:
2399:
2317:
2313:
2307:
2300:
2224:
2218:
2192:
2186:
2146:
2140:
2114:
2108:
2071:
2065:
1977:
1971:
1941:
1935:
1889:
1883:
1829:
1823:
1791:
1785:
1727:
1721:
1694:
1688:
1654:
1648:
1590:
1584:
1525:
1522:
1516:
1443:
1437:
1339:
1333:
1310:
1304:
1275:
1246:
1243:
1237:
1231:
1222:
1216:
1213:
1207:
1140:
1134:
1124:
1121:
1115:
1012:
1006:
955:
949:
895:
889:
848:
842:
807:
801:
736:
730:
646:
640:
592:
586:
529:
523:
461:
455:
432:{\displaystyle f(x)\neq f(y).}
423:
417:
408:
402:
379:
373:
285:
279:
231:
225:
159:
155:
149:
142:
82:
76:
1:
4226:Uniform boundedness principle
2159:consisting of functions with
1259:for some continuous function
1177:is continuous. Furthermore,
3091:Singular value decomposition
2285:{\displaystyle K\subseteq X}
1740:is only weakly complete for
3856:{\displaystyle L^{\infty }}
3624:{\displaystyle ba(\Sigma )}
3493:Radially convex/Star-shaped
2330:{\displaystyle |f(x)|<r}
2086:Hewitt & Stromberg 1965
2015:Hewitt & Stromberg 1965
624:Positive linear functionals
618:Dunford & Schwartz 1958
248:with respect to this norm.(
4571:
4369:Invariant subspace problem
3983:{\displaystyle W(X,L^{p})}
2479:Real and abstract analysis
2123:{\displaystyle C_{00}(X),}
62:. This space, denoted by
4499:
4089:
3529:Algebraic interior (core)
3144:Cauchy–Schwarz inequality
2787:Function space Topologies
2528:Real and complex analysis
2450:{\displaystyle C_{0}(X).}
2411:{\displaystyle C_{00}(X)}
2201:{\displaystyle C_{0}(X),}
1287:{\displaystyle f:Y\to X.}
873:Stone–Weierstrass theorem
659:correspond to (positive)
4338:Spectrum of a C*-algebra
2469:Linear operators, Part I
2077:{\displaystyle C_{B}(X)}
1983:{\displaystyle C_{B}(X)}
346:{\displaystyle x,y\in X}
4435:Noncommutative geometry
2266:there is a compact set
2259:{\displaystyle r>0,}
1559:{\displaystyle \Delta }
1495:{\displaystyle \Delta }
1412:{\displaystyle \Delta }
4491:Tomita–Takesaki theory
4466:Approximation property
4410:Calculus of variations
3984:
3908:
3857:
3818:
3781:
3691:
3625:
2794:Banach–Mazur compactum
2584:Types of Banach spaces
2451:
2412:
2366:
2331:
2286:
2260:
2231:
2202:
2153:
2124:
2078:
2038:
2007:
1984:
1948:
1919:
1896:
1859:
1836:
1811:Banach–Alaoglu theorem
1801:
1754:
1734:
1701:
1661:
1621:
1597:
1560:
1540:
1496:
1476:
1453:
1413:
1386:
1366:
1346:
1317:
1288:
1253:
1191:
1171:
1147:
1089:
1069:
1042:
1022:
986:
962:
925:
905:
858:
814:
781:
743:
710:
683:
653:
602:
563:
539:
488:
468:
433:
386:
347:
315:
292:
238:
205:
170:
92:
48:
4486:Banach–Mazur distance
4449:Generalized functions
4010:Finite element method
4005:Differential operator
3985:
3909:
3858:
3819:
3782:
3692:
3626:
3466:Convex series related
3262:Abstract Wiener space
3189:hyperplane separation
2744:Minkowski functionals
2628:Polarization identity
2452:
2413:
2375:vanishing at infinity
2367:
2332:
2287:
2261:
2232:
2203:
2154:
2125:
2079:
2039:
2008:
1985:
1949:
1920:
1897:
1860:
1837:
1802:
1755:
1735:
1702:
1662:
1622:
1598:
1561:
1541:
1497:
1477:
1454:
1414:
1387:
1367:
1347:
1318:
1289:
1254:
1192:
1172:
1148:
1090:
1070:
1043:
1023:
987:
963:
926:
906:
859:
824:if and only if it is
815:
782:
765:Arzelà –Ascoli theorem
744:
711:
684:
654:
603:
564:
540:
507:continuous dual space
489:
469:
434:
387:
348:
316:
293:
239:
206:
171:
106:with norm defined by
93:
49:
18:mathematical analysis
4231:Kakutani fixed-point
4216:Riesz representation
3952:
3878:
3840:
3801:
3749:
3652:
3603:
3592:Absolute continuity
3246:Schauder fixed-point
3236:Riesz representation
3196:Kakutani fixed-point
3164:Freudenthal spectral
2650:L-semi-inner product
2471:, Wiley-Interscience
2422:
2386:
2341:
2296:
2270:
2241:
2230:{\displaystyle C(X)}
2212:
2173:
2152:{\displaystyle C(X)}
2134:
2095:
2052:
2028:
1994:
1958:
1947:{\displaystyle C(X)}
1929:
1906:
1895:{\displaystyle C(X)}
1877:
1846:
1835:{\displaystyle C(X)}
1817:
1775:
1744:
1711:
1678:
1638:
1611:
1574:
1550:
1506:
1486:
1463:
1427:
1403:
1376:
1356:
1345:{\displaystyle C(Y)}
1327:
1316:{\displaystyle C(X)}
1298:
1263:
1201:
1181:
1161:
1099:
1079:
1059:
1032:
996:
976:
939:
915:
879:
832:
791:
771:
720:
700:
670:
630:
577:
553:
513:
478:
445:
396:
357:
325:
305:
269:
215:
192:
110:
66:
38:
26:continuous functions
4545:Functional analysis
4415:Functional calculus
4374:Mahler's conjecture
4353:Von Neumann algebra
4067:Functional analysis
3675:
3413:measurable function
3363:Functional calculus
3226:Parseval's identity
3139:Bessel's inequality
3086:Polar decomposition
2865:Uniform convergence
2623:Inner product space
2493:Functional Analysis
1396:topological spaces.
1050:complex conjugation
186:uniform convergence
54:with values in the
22:functional analysis
4555:Types of functions
4440:Riemann hypothesis
4139:Topological vector
4025:Validated numerics
3980:
3936:Sobolev inequality
3904:
3853:
3814:
3777:
3706:Bounded variation
3687:
3655:
3640:Banach coordinate
3621:
3559:Minkowski addition
3221:M. Riesz extension
2701:Banach spaces are:
2447:
2408:
2362:
2327:
2282:
2256:
2227:
2198:
2149:
2120:
2074:
2034:
2006:{\displaystyle X.}
2003:
1980:
1944:
1918:{\displaystyle X.}
1915:
1892:
1858:{\displaystyle X.}
1855:
1832:
1797:
1750:
1730:
1697:
1657:
1617:
1593:
1556:
1536:
1492:
1475:{\displaystyle X.}
1472:
1449:
1409:
1382:
1362:
1342:
1313:
1294:In particular, if
1284:
1249:
1187:
1167:
1143:
1085:
1065:
1038:
1018:
982:
958:
921:
901:
854:
822:relatively compact
810:
777:
739:
716:is infinite, then
706:
682:{\displaystyle X,}
679:
649:
598:
559:
535:
484:
464:
429:
382:
343:
311:
288:
234:
204:{\displaystyle X.}
201:
166:
140:
88:
44:
4517:
4516:
4420:Integral operator
4197:
4196:
4033:
4032:
3745:Morrey–Campanato
3727:compact Hausdorff
3574:Relative interior
3428:Absolutely convex
3395:Projection-valued
3004:Strictly singular
2930:on Hilbert spaces
2691:of Hilbert spaces
2507:978-0-07-054236-5
2481:, Springer-Verlag
2037:{\displaystyle X}
1753:{\displaystyle X}
1620:{\displaystyle X}
1605:Gelfand transform
1385:{\displaystyle Y}
1365:{\displaystyle X}
1190:{\displaystyle F}
1170:{\displaystyle F}
1088:{\displaystyle Y}
1068:{\displaystyle X}
1041:{\displaystyle A}
985:{\displaystyle A}
924:{\displaystyle A}
780:{\displaystyle K}
709:{\displaystyle X}
562:{\displaystyle X}
487:{\displaystyle X}
314:{\displaystyle X}
125:
47:{\displaystyle X}
20:, and especially
4562:
4535:Complex analysis
4507:
4506:
4425:Jones polynomial
4343:Operator algebra
4087:
4060:
4053:
4046:
4037:
3989:
3987:
3986:
3981:
3976:
3975:
3943:Triebel–Lizorkin
3913:
3911:
3910:
3905:
3903:
3899:
3898:
3893:
3862:
3860:
3859:
3854:
3852:
3851:
3823:
3821:
3820:
3815:
3813:
3812:
3786:
3784:
3783:
3778:
3767:
3766:
3696:
3694:
3693:
3688:
3683:
3674:
3669:
3630:
3628:
3627:
3622:
3483:
3461:
3443:Balanced/Circled
3241:Robinson-Ursescu
3159:Eberlein–Šmulian
3079:Spectral theorem
2875:Linear operators
2672:Uniformly smooth
2569:
2562:
2555:
2546:
2540:
2519:
2482:
2472:
2456:
2454:
2453:
2448:
2434:
2433:
2417:
2415:
2414:
2409:
2398:
2397:
2371:
2369:
2368:
2363:
2336:
2334:
2333:
2328:
2320:
2303:
2291:
2289:
2288:
2283:
2265:
2263:
2262:
2257:
2236:
2234:
2233:
2228:
2207:
2205:
2204:
2199:
2185:
2184:
2158:
2156:
2155:
2150:
2129:
2127:
2126:
2121:
2107:
2106:
2083:
2081:
2080:
2075:
2064:
2063:
2043:
2041:
2040:
2035:
2012:
2010:
2009:
2004:
1989:
1987:
1986:
1981:
1970:
1969:
1953:
1951:
1950:
1945:
1924:
1922:
1921:
1916:
1901:
1899:
1898:
1893:
1864:
1862:
1861:
1856:
1841:
1839:
1838:
1833:
1806:
1804:
1803:
1798:
1784:
1783:
1759:
1757:
1756:
1751:
1739:
1737:
1736:
1731:
1720:
1719:
1706:
1704:
1703:
1698:
1687:
1686:
1666:
1664:
1663:
1658:
1647:
1646:
1626:
1624:
1623:
1618:
1602:
1600:
1599:
1594:
1583:
1582:
1568:initial topology
1565:
1563:
1562:
1557:
1545:
1543:
1542:
1537:
1532:
1515:
1514:
1501:
1499:
1498:
1493:
1481:
1479:
1478:
1473:
1458:
1456:
1455:
1450:
1436:
1435:
1419:be the space of
1418:
1416:
1415:
1410:
1391:
1389:
1388:
1383:
1371:
1369:
1368:
1363:
1351:
1349:
1348:
1343:
1322:
1320:
1319:
1314:
1293:
1291:
1290:
1285:
1258:
1256:
1255:
1250:
1196:
1194:
1193:
1188:
1176:
1174:
1173:
1168:
1152:
1150:
1149:
1144:
1133:
1132:
1114:
1113:
1094:
1092:
1091:
1086:
1074:
1072:
1071:
1066:
1048:is closed under
1047:
1045:
1044:
1039:
1027:
1025:
1024:
1019:
1005:
1004:
991:
989:
988:
983:
967:
965:
964:
959:
948:
947:
930:
928:
927:
922:
910:
908:
907:
902:
888:
887:
863:
861:
860:
855:
841:
840:
819:
817:
816:
811:
800:
799:
786:
784:
783:
778:
767:holds: A subset
748:
746:
745:
740:
729:
728:
715:
713:
712:
707:
688:
686:
685:
680:
658:
656:
655:
650:
639:
638:
607:
605:
604:
599:
568:
566:
565:
560:
544:
542:
541:
536:
522:
521:
493:
491:
490:
485:
473:
471:
470:
465:
454:
453:
438:
436:
435:
430:
391:
389:
388:
383:
372:
371:
352:
350:
349:
344:
320:
318:
317:
312:
299:separates points
297:
295:
294:
289:
278:
277:
243:
241:
240:
235:
224:
223:
210:
208:
207:
202:
188:of functions on
175:
173:
172:
167:
162:
145:
139:
97:
95:
94:
89:
75:
74:
53:
51:
50:
45:
4570:
4569:
4565:
4564:
4563:
4561:
4560:
4559:
4520:
4519:
4518:
4513:
4495:
4459:Advanced topics
4454:
4378:
4357:
4316:
4282:Hilbert–Schmidt
4255:
4246:Gelfand–Naimark
4193:
4143:
4078:
4064:
4034:
4029:
3993:
3967:
3950:
3949:
3948:Wiener amalgam
3918:Segal–Bargmann
3888:
3884:
3876:
3875:
3843:
3838:
3837:
3804:
3799:
3798:
3752:
3747:
3746:
3701:Birnbaum–Orlicz
3650:
3649:
3601:
3600:
3578:
3534:Bounding points
3507:
3481:
3459:
3416:
3267:Banach manifold
3250:
3174:Gelfand–Naimark
3095:
3069:Spectral theory
3037:Banach algebras
3029:Operator theory
3023:
2984:Pseudo-monotone
2967:Hilbert–Schmidt
2947:Densely defined
2869:
2782:
2696:
2579:
2573:
2538:
2530:, McGraw-Hill,
2522:
2508:
2486:
2476:
2466:
2463:
2425:
2420:
2419:
2389:
2384:
2383:
2382:The closure of
2339:
2338:
2294:
2293:
2268:
2267:
2239:
2238:
2210:
2209:
2176:
2171:
2170:
2161:compact support
2132:
2131:
2098:
2093:
2092:
2055:
2050:
2049:
2046:locally compact
2026:
2025:
2017:, Theorem 7.9)
1992:
1991:
1961:
1956:
1955:
1927:
1926:
1904:
1903:
1875:
1874:
1871:
1869:Generalizations
1844:
1843:
1815:
1814:
1773:
1772:
1771:on the dual of
1742:
1741:
1709:
1708:
1676:
1675:
1636:
1635:
1609:
1608:
1572:
1571:
1548:
1547:
1504:
1503:
1484:
1483:
1461:
1460:
1425:
1424:
1401:
1400:
1374:
1373:
1354:
1353:
1325:
1324:
1296:
1295:
1261:
1260:
1199:
1198:
1179:
1178:
1159:
1158:
1097:
1096:
1077:
1076:
1057:
1056:
1030:
1029:
994:
993:
974:
973:
937:
936:
913:
912:
877:
876:
830:
829:
828:in the norm of
789:
788:
769:
768:
718:
717:
698:
697:
668:
667:
628:
627:
610:total variation
575:
574:
551:
550:
511:
510:
496:locally compact
476:
475:
443:
442:
394:
393:
355:
354:
323:
322:
303:
302:
267:
266:
263:Urysohn's lemma
258:
213:
212:
190:
189:
108:
107:
64:
63:
60:complex numbers
36:
35:
33:Hausdorff space
12:
11:
5:
4568:
4566:
4558:
4557:
4552:
4547:
4542:
4537:
4532:
4522:
4521:
4515:
4514:
4512:
4511:
4500:
4497:
4496:
4494:
4493:
4488:
4483:
4478:
4476:Choquet theory
4473:
4468:
4462:
4460:
4456:
4455:
4453:
4452:
4442:
4437:
4432:
4427:
4422:
4417:
4412:
4407:
4402:
4397:
4392:
4386:
4384:
4380:
4379:
4377:
4376:
4371:
4365:
4363:
4359:
4358:
4356:
4355:
4350:
4345:
4340:
4335:
4330:
4328:Banach algebra
4324:
4322:
4318:
4317:
4315:
4314:
4309:
4304:
4299:
4294:
4289:
4284:
4279:
4274:
4269:
4263:
4261:
4257:
4256:
4254:
4253:
4251:Banach–Alaoglu
4248:
4243:
4238:
4233:
4228:
4223:
4218:
4213:
4207:
4205:
4199:
4198:
4195:
4194:
4192:
4191:
4186:
4181:
4179:Locally convex
4176:
4162:
4157:
4151:
4149:
4145:
4144:
4142:
4141:
4136:
4131:
4126:
4121:
4116:
4111:
4106:
4101:
4096:
4090:
4084:
4080:
4079:
4065:
4063:
4062:
4055:
4048:
4040:
4031:
4030:
4028:
4027:
4022:
4017:
4012:
4007:
4001:
3999:
3995:
3994:
3992:
3991:
3979:
3974:
3970:
3966:
3963:
3960:
3957:
3945:
3940:
3939:
3938:
3928:
3926:Sequence space
3923:
3915:
3902:
3897:
3892:
3887:
3883:
3871:
3870:
3869:
3864:
3850:
3846:
3827:
3826:
3825:
3811:
3807:
3788:
3776:
3773:
3770:
3765:
3762:
3759:
3755:
3742:
3734:
3729:
3716:
3711:
3703:
3698:
3686:
3682:
3678:
3673:
3668:
3665:
3662:
3658:
3645:
3637:
3632:
3620:
3617:
3614:
3611:
3608:
3597:
3588:
3586:
3580:
3579:
3577:
3576:
3566:
3561:
3556:
3551:
3546:
3541:
3536:
3531:
3521:
3515:
3513:
3509:
3508:
3506:
3505:
3500:
3495:
3490:
3485:
3477:
3463:
3455:
3450:
3445:
3440:
3435:
3430:
3424:
3422:
3418:
3417:
3415:
3414:
3404:
3403:
3402:
3397:
3392:
3382:
3381:
3380:
3375:
3370:
3360:
3359:
3358:
3353:
3348:
3343:
3341:Gelfand–Pettis
3338:
3333:
3323:
3322:
3321:
3316:
3311:
3306:
3301:
3291:
3286:
3281:
3276:
3275:
3274:
3264:
3258:
3256:
3252:
3251:
3249:
3248:
3243:
3238:
3233:
3228:
3223:
3218:
3213:
3208:
3203:
3198:
3193:
3192:
3191:
3181:
3176:
3171:
3166:
3161:
3156:
3151:
3146:
3141:
3136:
3131:
3126:
3121:
3116:
3114:Banach–Alaoglu
3111:
3109:Anderson–Kadec
3105:
3103:
3097:
3096:
3094:
3093:
3088:
3083:
3082:
3081:
3076:
3066:
3065:
3064:
3059:
3049:
3047:Operator space
3044:
3039:
3033:
3031:
3025:
3024:
3022:
3021:
3016:
3011:
3006:
3001:
2996:
2991:
2986:
2981:
2980:
2979:
2969:
2964:
2963:
2962:
2957:
2949:
2944:
2934:
2933:
2932:
2922:
2917:
2907:
2906:
2905:
2900:
2895:
2885:
2879:
2877:
2871:
2870:
2868:
2867:
2862:
2857:
2856:
2855:
2850:
2840:
2839:
2838:
2833:
2823:
2818:
2813:
2812:
2811:
2801:
2796:
2790:
2788:
2784:
2783:
2781:
2780:
2775:
2770:
2769:
2768:
2758:
2753:
2748:
2747:
2746:
2735:Locally convex
2732:
2731:
2730:
2720:
2715:
2710:
2704:
2702:
2698:
2697:
2695:
2694:
2687:Tensor product
2680:
2674:
2669:
2663:
2658:
2652:
2647:
2642:
2632:
2631:
2630:
2625:
2615:
2610:
2608:Banach lattice
2605:
2604:
2603:
2593:
2587:
2585:
2581:
2580:
2574:
2572:
2571:
2564:
2557:
2549:
2543:
2542:
2536:
2520:
2506:
2484:
2474:
2462:
2459:
2446:
2443:
2440:
2437:
2432:
2428:
2407:
2404:
2401:
2396:
2392:
2380:
2379:
2361:
2358:
2355:
2352:
2349:
2346:
2326:
2323:
2319:
2315:
2312:
2309:
2306:
2302:
2281:
2278:
2275:
2255:
2252:
2249:
2246:
2226:
2223:
2220:
2217:
2208:the subset of
2197:
2194:
2191:
2188:
2183:
2179:
2168:
2148:
2145:
2142:
2139:
2130:the subset of
2119:
2116:
2113:
2110:
2105:
2101:
2073:
2070:
2067:
2062:
2058:
2033:
2022:measure theory
2002:
1999:
1979:
1976:
1973:
1968:
1964:
1943:
1940:
1937:
1934:
1914:
1911:
1891:
1888:
1885:
1882:
1870:
1867:
1866:
1865:
1854:
1851:
1831:
1828:
1825:
1822:
1807:
1796:
1793:
1790:
1787:
1782:
1769:weak* topology
1765:vague topology
1761:
1749:
1729:
1726:
1723:
1718:
1696:
1693:
1690:
1685:
1656:
1653:
1650:
1645:
1634:A sequence in
1632:
1616:
1603:(that is, the
1592:
1589:
1586:
1581:
1555:
1535:
1531:
1527:
1524:
1521:
1518:
1513:
1491:
1471:
1468:
1448:
1445:
1442:
1439:
1434:
1421:maximal ideals
1408:
1397:
1381:
1361:
1341:
1338:
1335:
1332:
1312:
1309:
1306:
1303:
1283:
1280:
1277:
1274:
1271:
1268:
1248:
1245:
1242:
1239:
1236:
1233:
1230:
1227:
1224:
1221:
1218:
1215:
1212:
1209:
1206:
1186:
1166:
1142:
1139:
1136:
1131:
1126:
1123:
1120:
1117:
1112:
1107:
1104:
1084:
1064:
1053:
1037:
1017:
1014:
1011:
1008:
1003:
981:
957:
954:
951:
946:
920:
900:
897:
894:
891:
886:
869:
866:equicontinuous
853:
850:
847:
844:
839:
809:
806:
803:
798:
776:
761:
738:
735:
732:
727:
705:
694:
678:
675:
664:Borel measures
648:
645:
642:
637:
621:
597:
594:
591:
588:
585:
582:
573:), denoted by
571:Borel measures
558:
547:Radon measures
534:
531:
528:
525:
520:
499:
483:
463:
460:
457:
452:
439:
428:
425:
422:
419:
416:
413:
410:
407:
404:
401:
381:
378:
375:
370:
365:
362:
342:
339:
336:
333:
330:
310:
287:
284:
281:
276:
257:
254:
246:Banach algebra
233:
230:
227:
222:
200:
197:
165:
161:
157:
154:
151:
148:
144:
138:
135:
132:
128:
124:
121:
118:
115:
87:
84:
81:
78:
73:
43:
13:
10:
9:
6:
4:
3:
2:
4567:
4556:
4553:
4551:
4550:Real analysis
4548:
4546:
4543:
4541:
4538:
4536:
4533:
4531:
4530:Banach spaces
4528:
4527:
4525:
4510:
4502:
4501:
4498:
4492:
4489:
4487:
4484:
4482:
4481:Weak topology
4479:
4477:
4474:
4472:
4469:
4467:
4464:
4463:
4461:
4457:
4450:
4446:
4443:
4441:
4438:
4436:
4433:
4431:
4428:
4426:
4423:
4421:
4418:
4416:
4413:
4411:
4408:
4406:
4405:Index theorem
4403:
4401:
4398:
4396:
4393:
4391:
4388:
4387:
4385:
4381:
4375:
4372:
4370:
4367:
4366:
4364:
4362:Open problems
4360:
4354:
4351:
4349:
4346:
4344:
4341:
4339:
4336:
4334:
4331:
4329:
4326:
4325:
4323:
4319:
4313:
4310:
4308:
4305:
4303:
4300:
4298:
4295:
4293:
4290:
4288:
4285:
4283:
4280:
4278:
4275:
4273:
4270:
4268:
4265:
4264:
4262:
4258:
4252:
4249:
4247:
4244:
4242:
4239:
4237:
4234:
4232:
4229:
4227:
4224:
4222:
4219:
4217:
4214:
4212:
4209:
4208:
4206:
4204:
4200:
4190:
4187:
4185:
4182:
4180:
4177:
4174:
4170:
4166:
4163:
4161:
4158:
4156:
4153:
4152:
4150:
4146:
4140:
4137:
4135:
4132:
4130:
4127:
4125:
4122:
4120:
4117:
4115:
4112:
4110:
4107:
4105:
4102:
4100:
4097:
4095:
4092:
4091:
4088:
4085:
4081:
4076:
4072:
4068:
4061:
4056:
4054:
4049:
4047:
4042:
4041:
4038:
4026:
4023:
4021:
4018:
4016:
4013:
4011:
4008:
4006:
4003:
4002:
4000:
3996:
3990:
3972:
3968:
3964:
3961:
3955:
3946:
3944:
3941:
3937:
3934:
3933:
3932:
3929:
3927:
3924:
3922:
3921:
3916:
3914:
3900:
3895:
3885:
3881:
3872:
3868:
3865:
3863:
3844:
3835:
3834:
3833:
3832:
3828:
3824:
3805:
3796:
3795:
3794:
3793:
3789:
3787:
3763:
3760:
3757:
3753:
3743:
3741:
3740:
3735:
3733:
3730:
3728:
3726:
3722:
3717:
3715:
3712:
3710:
3709:
3704:
3702:
3699:
3697:
3671:
3666:
3663:
3660:
3656:
3646:
3644:
3643:
3638:
3636:
3633:
3631:
3609:
3606:
3598:
3596:
3595:
3590:
3589:
3587:
3585:
3581:
3575:
3571:
3567:
3565:
3562:
3560:
3557:
3555:
3552:
3550:
3547:
3545:
3544:Extreme point
3542:
3540:
3537:
3535:
3532:
3530:
3526:
3522:
3520:
3517:
3516:
3514:
3510:
3504:
3501:
3499:
3496:
3494:
3491:
3489:
3486:
3484:
3478:
3475:
3471:
3467:
3464:
3462:
3456:
3454:
3451:
3449:
3446:
3444:
3441:
3439:
3436:
3434:
3431:
3429:
3426:
3425:
3423:
3421:Types of sets
3419:
3412:
3408:
3405:
3401:
3398:
3396:
3393:
3391:
3388:
3387:
3386:
3383:
3379:
3376:
3374:
3371:
3369:
3366:
3365:
3364:
3361:
3357:
3354:
3352:
3349:
3347:
3344:
3342:
3339:
3337:
3334:
3332:
3329:
3328:
3327:
3324:
3320:
3317:
3315:
3312:
3310:
3307:
3305:
3302:
3300:
3297:
3296:
3295:
3292:
3290:
3287:
3285:
3284:Convex series
3282:
3280:
3279:Bochner space
3277:
3273:
3270:
3269:
3268:
3265:
3263:
3260:
3259:
3257:
3253:
3247:
3244:
3242:
3239:
3237:
3234:
3232:
3231:Riesz's lemma
3229:
3227:
3224:
3222:
3219:
3217:
3216:Mazur's lemma
3214:
3212:
3209:
3207:
3204:
3202:
3199:
3197:
3194:
3190:
3187:
3186:
3185:
3182:
3180:
3177:
3175:
3172:
3170:
3169:Gelfand–Mazur
3167:
3165:
3162:
3160:
3157:
3155:
3152:
3150:
3147:
3145:
3142:
3140:
3137:
3135:
3132:
3130:
3127:
3125:
3122:
3120:
3117:
3115:
3112:
3110:
3107:
3106:
3104:
3102:
3098:
3092:
3089:
3087:
3084:
3080:
3077:
3075:
3072:
3071:
3070:
3067:
3063:
3060:
3058:
3055:
3054:
3053:
3050:
3048:
3045:
3043:
3040:
3038:
3035:
3034:
3032:
3030:
3026:
3020:
3017:
3015:
3012:
3010:
3007:
3005:
3002:
3000:
2997:
2995:
2992:
2990:
2987:
2985:
2982:
2978:
2975:
2974:
2973:
2970:
2968:
2965:
2961:
2958:
2956:
2953:
2952:
2950:
2948:
2945:
2943:
2939:
2935:
2931:
2928:
2927:
2926:
2923:
2921:
2918:
2916:
2912:
2908:
2904:
2901:
2899:
2896:
2894:
2891:
2890:
2889:
2886:
2884:
2881:
2880:
2878:
2876:
2872:
2866:
2863:
2861:
2858:
2854:
2851:
2849:
2846:
2845:
2844:
2841:
2837:
2834:
2832:
2829:
2828:
2827:
2824:
2822:
2819:
2817:
2814:
2810:
2807:
2806:
2805:
2802:
2800:
2797:
2795:
2792:
2791:
2789:
2785:
2779:
2776:
2774:
2771:
2767:
2764:
2763:
2762:
2759:
2757:
2754:
2752:
2749:
2745:
2741:
2738:
2737:
2736:
2733:
2729:
2726:
2725:
2724:
2721:
2719:
2716:
2714:
2711:
2709:
2706:
2705:
2703:
2699:
2692:
2688:
2684:
2681:
2679:
2675:
2673:
2670:
2668:) convex
2667:
2664:
2662:
2659:
2657:
2653:
2651:
2648:
2646:
2643:
2641:
2637:
2633:
2629:
2626:
2624:
2621:
2620:
2619:
2616:
2614:
2613:Grothendieck
2611:
2609:
2606:
2602:
2599:
2598:
2597:
2594:
2592:
2589:
2588:
2586:
2582:
2577:
2570:
2565:
2563:
2558:
2556:
2551:
2550:
2547:
2539:
2537:0-07-054234-1
2533:
2529:
2525:
2524:Rudin, Walter
2521:
2517:
2513:
2509:
2503:
2499:
2495:
2494:
2489:
2488:Rudin, Walter
2485:
2480:
2475:
2470:
2465:
2464:
2460:
2458:
2444:
2438:
2430:
2426:
2418:is precisely
2402:
2394:
2390:
2377:
2376:
2359:
2356:
2350:
2347:
2344:
2324:
2321:
2310:
2304:
2279:
2276:
2273:
2253:
2250:
2247:
2244:
2221:
2215:
2195:
2189:
2181:
2177:
2169:
2166:
2162:
2143:
2137:
2117:
2111:
2103:
2099:
2091:
2090:
2089:
2087:
2068:
2060:
2056:
2047:
2031:
2023:
2018:
2016:
2000:
1997:
1974:
1966:
1962:
1938:
1932:
1912:
1909:
1886:
1880:
1868:
1852:
1849:
1826:
1820:
1812:
1808:
1794:
1788:
1770:
1766:
1762:
1760:a finite set.
1747:
1724:
1691:
1673:
1670:
1651:
1633:
1630:
1614:
1606:
1587:
1569:
1533:
1519:
1482:Furthermore,
1469:
1466:
1446:
1440:
1422:
1398:
1395:
1379:
1359:
1336:
1330:
1307:
1301:
1281:
1278:
1272:
1269:
1266:
1240:
1234:
1228:
1225:
1219:
1210:
1204:
1197:has the form
1184:
1164:
1156:
1137:
1118:
1105:
1102:
1082:
1062:
1054:
1051:
1035:
1015:
1009:
979:
971:
952:
934:
918:
898:
892:
874:
870:
867:
851:
845:
827:
823:
804:
774:
766:
762:
759:
756:
752:
733:
703:
695:
692:
676:
673:
665:
662:
643:
625:
622:
619:
615:
611:
595:
589:
583:
580:
572:
556:
548:
532:
526:
508:
504:
500:
497:
481:
458:
440:
426:
420:
414:
411:
405:
399:
376:
363:
360:
340:
337:
334:
331:
328:
308:
300:
282:
264:
260:
259:
255:
253:
251:
247:
228:
198:
195:
187:
183:
179:
163:
152:
146:
136:
133:
130:
122:
116:
105:
101:
85:
79:
61:
57:
41:
34:
31:
27:
23:
19:
4471:Balanced set
4445:Distribution
4383:Applications
4236:Krein–Milman
4221:Closed graph
3998:Applications
3919:
3830:
3791:
3738:
3724:
3720:
3718:
3707:
3641:
3593:
3480:Linear cone
3473:
3469:
3458:Convex cone
3351:Paley–Wiener
3211:Mackey–Arens
3201:Krein–Milman
3154:Closed range
3149:Closed graph
3119:Banach–Mazur
2999:Self-adjoint
2903:sesquilinear
2636:Polynomially
2576:Banach space
2527:
2492:
2478:
2468:
2381:
2373:
2164:
2019:
1872:
1394:homeomorphic
1155:homomorphism
753:, nor is it
693:, Chapter 2)
178:uniform norm
104:normed space
100:vector space
15:
4400:Heat kernel
4390:Hardy space
4297:Trace class
4211:Hahn–Banach
4173:Topological
3719:Continuous
3554:Linear span
3539:Convex hull
3519:Affine hull
3378:holomorphic
3314:holomorphic
3294:Derivatives
3184:Hahn–Banach
3124:Banach–Saks
3042:C*-algebras
3009:Trace class
2972:Functionals
2860:Ultrastrong
2773:Quasinormed
4524:Categories
4333:C*-algebra
4148:Properties
3472:), and (Hw
3373:continuous
3309:functional
3057:C*-algebra
2942:Continuous
2804:Dual space
2778:Stereotype
2756:Metrizable
2683:Projective
2461:References
2292:such that
1873:The space
1629:Rudin 1973
875:holds for
691:Rudin 1966
620:, §IV.6.3)
441:The space
392:such that
256:Properties
250:Rudin 1973
211:The space
4307:Unbounded
4302:Transpose
4260:Operators
4189:Separable
4184:Reflexive
4169:Algebraic
4155:Barrelled
3931:Sobolev W
3874:Schwartz
3849:∞
3810:∞
3806:ℓ
3772:Ω
3758:λ
3616:Σ
3498:Symmetric
3433:Absorbing
3346:regulated
3326:Integrals
3179:Goldstine
3014:Transpose
2951:Fredholm
2821:Ultraweak
2809:Dual norm
2740:Seminorms
2708:Barrelled
2678:Injective
2666:Uniformly
2640:Reflexive
2354:∖
2348:∈
2277:⊆
2088:, §II.7)
1842:for some
1631:, §11.13)
1607:). Then
1566:with the
1554:Δ
1526:→
1490:Δ
1407:Δ
1276:→
1125:→
751:reflexive
614:ba spaces
584:
569:(regular
412:≠
364:∈
338:∈
252:, §11.3)
134:∈
120:‖
114:‖
4509:Category
4321:Algebras
4203:Theorems
4160:Complete
4129:Schwartz
4075:glossary
3867:weighted
3737:Hilbert
3714:Bs space
3584:Examples
3549:Interior
3525:Relative
3503:Zonotope
3482:(subset)
3460:(subset)
3411:Strongly
3390:Lebesgue
3385:Measures
3255:Analysis
3101:Theorems
3052:Spectrum
2977:positive
2960:operator
2898:operator
2888:Bilinear
2853:operator
2836:operator
2816:Operator
2713:Complete
2661:Strictly
2526:(1966),
2516:21163277
2490:(1991).
2337:for all
758:complete
182:topology
4312:Unitary
4292:Nuclear
4277:Compact
4272:Bounded
4267:Adjoint
4241:Min–max
4134:Sobolev
4119:Nuclear
4109:Hilbert
4104:Fréchet
4069: (
3732:Hardy H
3635:c space
3572:)
3527:)
3448:Bounded
3336:Dunford
3331:Bochner
3304:Gateaux
3299:Fréchet
3074:of ODEs
3019:Unitary
2994:Nuclear
2925:Compact
2915:Bounded
2883:Adjoint
2723:Fréchet
2718:F-space
2689: (
2685:)
2638:)
2618:Hilbert
2591:Asplund
1767:is the
970:closure
933:subring
826:bounded
749:is not
661:regular
30:compact
4287:Normal
4124:Orlicz
4114:Hölder
4094:Banach
4083:Spaces
4071:topics
3648:Besov
3488:Radial
3453:Convex
3438:Affine
3407:Weakly
3400:Vector
3272:bundle
3062:radius
2989:Normal
2955:kernel
2920:Closed
2843:Strong
2761:Normed
2751:Mackey
2596:Banach
2578:topics
2534:
2514:
2504:
1672:Cauchy
1669:weakly
1546:Equip
755:weakly
4099:Besov
3723:with
3570:Quasi
3564:Polar
3368:Borel
3319:quasi
2848:polar
2831:polar
2645:Riesz
2044:is a
1153:is a
931:is a
321:: If
244:is a
98:is a
28:on a
4447:(or
4165:Dual
3721:C(K)
3356:weak
2893:form
2826:Weak
2799:Dual
2766:norm
2728:tame
2601:list
2532:ISBN
2512:OCLC
2502:ISBN
2322:<
2248:>
1809:The
1763:The
1399:Let
1392:are
1372:and
1323:and
1075:and
871:The
864:and
763:The
501:The
176:the
56:real
2938:Dis
2084:: (
1667:is
1423:in
1055:If
992:is
972:of
935:of
820:is
787:of
696:If
666:on
626:on
616:. (
581:rca
549:on
509:of
301:of
261:By
184:of
127:sup
58:or
16:In
4526::
4073:–
3708:BV
3642:BK
3594:AC
3476:))
3409:/
2911:Un
2510:.
2500:.
2395:00
2104:00
265:,
4451:)
4175:)
4171:/
4167:(
4077:)
4059:e
4052:t
4045:v
3978:)
3973:p
3969:L
3965:,
3962:X
3959:(
3956:W
3920:F
3901:)
3896:n
3891:R
3886:(
3882:S
3845:L
3831:L
3792:â„“
3775:)
3769:(
3764:p
3761:,
3754:L
3739:H
3725:K
3685:)
3681:R
3677:(
3672:s
3667:q
3664:,
3661:p
3657:B
3619:)
3613:(
3610:a
3607:b
3568:(
3523:(
3474:x
3470:x
2940:)
2936:(
2913:)
2909:(
2742:/
2693:)
2676:(
2656:B
2654:(
2634:(
2568:e
2561:t
2554:v
2541:.
2518:.
2483:.
2473:.
2445:.
2442:)
2439:X
2436:(
2431:0
2427:C
2406:)
2403:X
2400:(
2391:C
2378:.
2360:.
2357:K
2351:X
2345:x
2325:r
2318:|
2314:)
2311:x
2308:(
2305:f
2301:|
2280:X
2274:K
2254:,
2251:0
2245:r
2225:)
2222:X
2219:(
2216:C
2196:,
2193:)
2190:X
2187:(
2182:0
2178:C
2167:.
2147:)
2144:X
2141:(
2138:C
2118:,
2115:)
2112:X
2109:(
2100:C
2072:)
2069:X
2066:(
2061:B
2057:C
2032:X
2001:.
1998:X
1978:)
1975:X
1972:(
1967:B
1963:C
1942:)
1939:X
1936:(
1933:C
1913:.
1910:X
1890:)
1887:X
1884:(
1881:C
1853:.
1850:X
1830:)
1827:X
1824:(
1821:C
1795:.
1792:)
1789:X
1786:(
1781:C
1748:X
1728:)
1725:X
1722:(
1717:C
1695:)
1692:X
1689:(
1684:C
1655:)
1652:X
1649:(
1644:C
1615:X
1591:)
1588:X
1585:(
1580:C
1534:.
1530:C
1523:)
1520:X
1517:(
1512:C
1470:.
1467:X
1447:.
1444:)
1441:X
1438:(
1433:C
1380:Y
1360:X
1340:)
1337:Y
1334:(
1331:C
1311:)
1308:X
1305:(
1302:C
1282:.
1279:X
1273:Y
1270::
1267:f
1247:)
1244:)
1241:y
1238:(
1235:f
1232:(
1229:h
1226:=
1223:)
1220:y
1217:(
1214:)
1211:h
1208:(
1205:F
1185:F
1165:F
1141:)
1138:Y
1135:(
1130:C
1122:)
1119:X
1116:(
1111:C
1106::
1103:F
1083:Y
1063:X
1052:.
1036:A
1016:.
1013:)
1010:X
1007:(
1002:C
980:A
956:)
953:X
950:(
945:C
919:A
899:.
896:)
893:X
890:(
885:C
868:.
852:,
849:)
846:X
843:(
838:C
808:)
805:X
802:(
797:C
775:K
760:.
737:)
734:X
731:(
726:C
704:X
677:,
674:X
647:)
644:X
641:(
636:C
596:.
593:)
590:X
587:(
557:X
533:.
530:)
527:X
524:(
519:C
498:.
482:X
462:)
459:X
456:(
451:C
427:.
424:)
421:y
418:(
415:f
409:)
406:x
403:(
400:f
380:)
377:X
374:(
369:C
361:f
341:X
335:y
332:,
329:x
309:X
286:)
283:X
280:(
275:C
232:)
229:X
226:(
221:C
199:.
196:X
164:,
160:|
156:)
153:x
150:(
147:f
143:|
137:X
131:x
123:=
117:f
86:,
83:)
80:X
77:(
72:C
42:X
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