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Functional Analysis: Introductory Course on the Theory of Duality Topology-Bornology and its use in Functional Analysis
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Every neighborhood of the origin in a TVS is bornivorous. The convex hull, closed convex hull, and
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1329:. Translated by Chaljub, Orlando. New York: Gordon and Breach Science Publishers.
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1537:. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press.
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is a vector subspace of finite codimension in a locally convex space
1196:. Graduate Texts in Mathematics. Vol. 15. New York: Springer.
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Topological Vector Spaces: The Theory
Without Convexity Conditions
1165:. Lecture Notes in Mathematics. Vol. 639. Berlin New York:
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is locally bounded (i.e. maps bounded sets to bounded sets).
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Every bornivorous and infrabornivorous subset of a TVS is
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1601:. Mineola, New York: Dover Publications, Inc.
1533:Narici, Lawrence; Beckenstein, Edward (2011).
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425:space is infrabornivorous if and only if its
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1224:Topological Vector Spaces: Chapters 1–5
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2452:Uniform boundedness (Banach–Steinhaus)
1016:Bounded set (topological vector space)
736:as a vector space over the reals. If
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648:Examples and sufficient conditions
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2018:Topological quantum field theory
1295:. New York: Dover Publications.
729:{\displaystyle \mathbb {R} ^{2}}
2977:With the approximation property
1258:A Course in Functional Analysis
1192:Berberian, Sterling K. (1974).
938:{\displaystyle (-1,-1),(-1,1),}
102:{\displaystyle {\mathcal {B}}.}
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1070:Narici & Beckenstein 2011
523:{\displaystyle B\subseteq M.}
1563:; Wolff, Manfred P. (1999).
1461:Lecture Notes in Mathematics
2661:Radially convex/Star-shaped
2646:Pre-compact/Totally bounded
1455:Khaleelulla, S. M. (1982).
1422:Topological Vector Spaces I
1394:. Stuttgart: B.G. Teubner.
1291:Edwards, Robert E. (1995).
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2347:Continuous linear operator
1957:Invariant subspace problem
638:{\displaystyle B=C\cap M.}
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131:topological vector space
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2023:Noncommutative geometry
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1039:Ultrabornological space
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235:is a TVS then a subset
43:that has an associated
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1998:Calculus of variations
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1941:Von Neumann algebra
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1135:, pp. 371–423.
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1072:, pp. 441–457.
205:bornological spaces
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2875:(Pseudo)Metrizable
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1431:978-3-642-64988-2
1401:978-3-519-02224-4
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1220:Bourbaki, Nicolas
1203:978-0-387-90081-0
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990:{\displaystyle T}
876:{\displaystyle T}
856:{\displaystyle S}
836:{\displaystyle S}
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700:{\displaystyle X}
672:{\displaystyle X}
603:{\displaystyle X}
583:{\displaystyle C}
563:{\displaystyle M}
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494:{\displaystyle X}
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391:{\displaystyle X}
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2607:
2602:
2597:
2592:
2587:
2582:
2576:
2574:
2570:
2569:
2567:
2566:
2561:
2556:
2551:
2546:
2545:
2544:
2539:
2534:
2524:
2519:
2518:
2517:
2512:
2507:
2502:
2497:
2492:
2487:
2477:
2476:
2475:
2464:
2462:
2458:
2457:
2455:
2454:
2449:
2448:
2447:
2437:
2431:
2422:
2417:
2412:
2410:Banach–Alaoglu
2407:
2405:Anderson–Kadec
2401:
2399:
2393:
2392:
2390:
2389:
2384:
2379:
2374:
2369:
2364:
2359:
2354:
2349:
2344:
2339:
2333:
2331:
2330:Basic concepts
2327:
2326:
2320:
2318:
2317:
2310:
2303:
2295:
2286:
2285:
2283:
2282:
2277:
2267:
2262:
2252:
2241:
2239:
2238:Related spaces
2235:
2234:
2232:
2231:
2226:
2221:
2215:
2213:
2209:
2208:
2206:
2205:
2200:
2189:
2187:
2183:
2182:
2180:
2179:
2169:
2164:
2159:
2153:
2151:
2150:Basic concepts
2147:
2146:
2137:
2135:
2134:
2127:
2120:
2112:
2103:
2102:
2100:
2099:
2088:
2085:
2084:
2082:
2081:
2076:
2071:
2066:
2064:Choquet theory
2061:
2056:
2050:
2048:
2044:
2043:
2041:
2040:
2030:
2025:
2020:
2015:
2010:
2005:
2000:
1995:
1990:
1985:
1980:
1974:
1972:
1968:
1967:
1965:
1964:
1959:
1953:
1951:
1947:
1946:
1944:
1943:
1938:
1933:
1928:
1923:
1918:
1916:Banach algebra
1912:
1910:
1906:
1905:
1903:
1902:
1897:
1892:
1887:
1882:
1877:
1872:
1867:
1862:
1857:
1851:
1849:
1845:
1844:
1842:
1841:
1839:Banach–Alaoglu
1836:
1831:
1826:
1821:
1816:
1811:
1806:
1801:
1795:
1793:
1787:
1786:
1783:
1782:
1780:
1779:
1774:
1769:
1767:Locally convex
1764:
1750:
1745:
1739:
1737:
1733:
1732:
1730:
1729:
1724:
1719:
1714:
1709:
1704:
1699:
1694:
1689:
1684:
1678:
1672:
1668:
1667:
1653:
1651:
1650:
1643:
1636:
1628:
1622:
1621:
1607:
1591:
1577:
1557:
1544:978-1584888666
1543:
1530:
1516:
1487:
1473:
1452:
1430:
1414:
1400:
1387:
1365:
1349:
1335:
1315:
1301:
1288:
1274:
1250:
1236:
1216:
1202:
1189:
1175:
1156:
1153:
1150:
1149:
1137:
1125:
1110:
1098:
1096:, p. 443.
1086:
1084:, p. 442.
1074:
1054:
1053:
1051:
1048:
1047:
1046:
1041:
1036:
1031:
1025:
1019:
1013:
1002:
999:
986:
966:
963:
960:
957:
954:
934:
931:
928:
925:
922:
919:
916:
913:
910:
907:
904:
901:
898:
895:
892:
872:
852:
832:
812:
809:
806:
803:
800:
780:
777:
774:
771:
768:
765:
745:
723:
718:
696:
684:
681:
668:
649:
646:
634:
631:
628:
625:
622:
619:
599:
579:
559:
539:
519:
516:
513:
510:
490:
470:
444:
441:
436:compactivorous
431:locally convex
423:locally convex
387:
360:
357:
349:locally convex
330:
327:
316:bounded subset
300:
264:
244:
224:
212:
209:
188:
162:
142:
118:
98:
93:
57:
32:
15:
13:
10:
9:
6:
4:
3:
2:
3028:
3017:
3014:
3013:
3011:
2996:
2988:
2987:
2984:
2978:
2975:
2973:
2970:
2968:
2965:
2963:
2959:
2955:
2953:) convex
2952:
2949:
2947:
2944:
2942:
2938:
2936:
2933:
2931:
2928:
2926:
2925:Semi-complete
2923:
2921:
2918:
2916:
2913:
2911:
2907:
2904:
2902:
2898:
2896:
2893:
2891:
2888:
2886:
2883:
2881:
2878:
2876:
2873:
2871:
2868:
2866:
2863:
2861:
2858:
2856:
2853:
2851:
2848:
2846:
2843:
2841:
2840:Infrabarreled
2838:
2836:
2833:
2831:
2828:
2824:
2821:
2820:
2819:
2816:
2814:
2811:
2809:
2806:
2804:
2801:
2799:
2798:Distinguished
2796:
2794:
2791:
2789:
2786:
2784:
2781:
2779:
2776:
2774:
2770:
2766:
2764:
2761:
2759:
2755:
2751:
2749:
2746:
2744:
2741:
2739:
2736:
2735:
2733:
2731:Types of TVSs
2729:
2723:
2719:
2715:
2713:
2710:
2708:
2705:
2703:
2700:
2698:
2695:
2693:
2689:
2685:
2683:
2680:
2679:
2677:
2673:
2667:
2664:
2662:
2659:
2657:
2654:
2652:
2651:Prevalent/Shy
2649:
2647:
2644:
2642:
2641:Extreme point
2639:
2637:
2631:
2629:
2623:
2621:
2618:
2616:
2613:
2611:
2608:
2606:
2603:
2601:
2598:
2596:
2593:
2591:
2588:
2586:
2583:
2581:
2578:
2577:
2575:
2573:Types of sets
2571:
2565:
2562:
2560:
2557:
2555:
2552:
2550:
2547:
2543:
2540:
2538:
2535:
2533:
2530:
2529:
2528:
2525:
2523:
2520:
2516:
2515:Discontinuous
2513:
2511:
2508:
2506:
2503:
2501:
2498:
2496:
2493:
2491:
2488:
2486:
2483:
2482:
2481:
2478:
2474:
2471:
2470:
2469:
2466:
2465:
2463:
2459:
2453:
2450:
2446:
2443:
2442:
2441:
2438:
2435:
2432:
2430:
2426:
2423:
2421:
2418:
2416:
2413:
2411:
2408:
2406:
2403:
2402:
2400:
2398:
2394:
2388:
2385:
2383:
2380:
2378:
2375:
2373:
2372:Metrizability
2370:
2368:
2365:
2363:
2360:
2358:
2357:Fréchet space
2355:
2353:
2350:
2348:
2345:
2343:
2340:
2338:
2335:
2334:
2332:
2328:
2323:
2316:
2311:
2309:
2304:
2302:
2297:
2296:
2293:
2281:
2278:
2276:
2272:
2268:
2266:
2263:
2261:
2257:
2253:
2251:
2247:
2243:
2242:
2240:
2236:
2230:
2227:
2225:
2222:
2220:
2219:Barrelled set
2217:
2216:
2214:
2210:
2204:
2201:
2199:
2195:
2191:
2190:
2188:
2184:
2178:
2174:
2170:
2168:
2165:
2163:
2160:
2158:
2155:
2154:
2152:
2148:
2144:
2140:
2133:
2128:
2126:
2121:
2119:
2114:
2113:
2110:
2098:
2090:
2089:
2086:
2080:
2077:
2075:
2072:
2070:
2069:Weak topology
2067:
2065:
2062:
2060:
2057:
2055:
2052:
2051:
2049:
2045:
2038:
2034:
2031:
2029:
2026:
2024:
2021:
2019:
2016:
2014:
2011:
2009:
2006:
2004:
2001:
1999:
1996:
1994:
1993:Index theorem
1991:
1989:
1986:
1984:
1981:
1979:
1976:
1975:
1973:
1969:
1963:
1960:
1958:
1955:
1954:
1952:
1950:Open problems
1948:
1942:
1939:
1937:
1934:
1932:
1929:
1927:
1924:
1922:
1919:
1917:
1914:
1913:
1911:
1907:
1901:
1898:
1896:
1893:
1891:
1888:
1886:
1883:
1881:
1878:
1876:
1873:
1871:
1868:
1866:
1863:
1861:
1858:
1856:
1853:
1852:
1850:
1846:
1840:
1837:
1835:
1832:
1830:
1827:
1825:
1822:
1820:
1817:
1815:
1812:
1810:
1807:
1805:
1802:
1800:
1797:
1796:
1794:
1792:
1788:
1778:
1775:
1773:
1770:
1768:
1765:
1762:
1758:
1754:
1751:
1749:
1746:
1744:
1741:
1740:
1738:
1734:
1728:
1725:
1723:
1720:
1718:
1715:
1713:
1710:
1708:
1705:
1703:
1700:
1698:
1695:
1693:
1690:
1688:
1685:
1683:
1680:
1679:
1676:
1673:
1669:
1664:
1660:
1656:
1649:
1644:
1642:
1637:
1635:
1630:
1629:
1626:
1618:
1614:
1610:
1604:
1600:
1596:
1592:
1588:
1584:
1580:
1574:
1570:
1566:
1562:
1558:
1554:
1550:
1546:
1540:
1536:
1531:
1527:
1523:
1519:
1513:
1509:
1502:
1501:
1496:
1492:
1488:
1484:
1480:
1476:
1470:
1466:
1462:
1458:
1453:
1449:
1445:
1441:
1437:
1433:
1427:
1423:
1419:
1415:
1411:
1407:
1403:
1397:
1393:
1388:
1384:
1380:
1376:
1372:
1368:
1362:
1358:
1354:
1350:
1346:
1342:
1338:
1332:
1327:
1326:
1320:
1316:
1312:
1308:
1304:
1298:
1294:
1289:
1285:
1281:
1277:
1271:
1267:
1263:
1259:
1255:
1251:
1247:
1243:
1239:
1237:3-540-13627-4
1233:
1229:
1225:
1221:
1217:
1213:
1209:
1205:
1199:
1195:
1190:
1186:
1182:
1178:
1172:
1168:
1164:
1159:
1158:
1154:
1147:, p. 48.
1146:
1145:Wilansky 2013
1141:
1138:
1134:
1129:
1126:
1123:, p. 50.
1122:
1121:Wilansky 2013
1117:
1115:
1111:
1107:
1102:
1099:
1095:
1090:
1087:
1083:
1078:
1075:
1071:
1066:
1064:
1062:
1060:
1056:
1049:
1045:
1042:
1040:
1037:
1035:
1032:
1029:
1026:
1023:
1020:
1017:
1014:
1008:
1005:
1004:
1000:
998:
984:
961:
958:
955:
932:
926:
923:
920:
917:
911:
905:
902:
899:
896:
893:
870:
850:
830:
807:
804:
801:
775:
772:
769:
766:
743:
721:
694:
682:
680:
666:
657:
655:
654:balanced hull
647:
645:
632:
629:
626:
623:
620:
617:
597:
577:
557:
537:
517:
514:
511:
508:
488:
468:
459:
456:
454:
450:
442:
440:
432:
428:
424:
420:
415:
413:
409:
405:
385:
376:
374:
370:
358:
356:
354:
350:
346:
341:
328:
325:
317:
313:
298:
290:
282:
262:
242:
222:
210:
208:
206:
201:
199:
186:
176:
160:
140:
132:
116:
96:
81:
77:
73:
46:
30:
22:
2901:Polynomially
2830:Grothendieck
2823:tame Fréchet
2773:Bornological
2633:Linear cone
2625:Convex cone
2600:Banach disks
2542:Sesquilinear
2397:Main results
2387:Vector space
2342:Completeness
2337:Banach space
2223:
2059:Balanced set
2033:Distribution
1971:Applications
1824:Krein–Milman
1809:Closed graph
1598:
1564:
1534:
1499:
1456:
1421:
1391:
1356:
1324:
1292:
1257:
1223:
1193:
1162:
1155:Bibliography
1140:
1128:
1101:
1089:
1077:
686:
658:
651:
460:
457:
446:
416:
399:
377:
373:Banach disks
367:infrabounded
364:
362:
342:
284:
276:
214:
202:
174:
75:
71:
18:
2895:Quasinormed
2808:FK-AK space
2702:Linear span
2697:Convex hull
2682:Affine hull
2485:Almost open
2425:Hahn–Banach
2162:Bounded set
2139:Boundedness
1988:Heat kernel
1978:Hardy space
1885:Trace class
1799:Hahn–Banach
1761:Topological
412:Banach disk
371:if it maps
279:bornivorous
211:Definitions
175:bornivorous
72:bornivorous
2935:Stereotype
2793:(DF)-space
2788:Convenient
2527:Functional
2495:Continuous
2480:Linear map
2420:F. Riesz's
2362:Linear map
1921:C*-algebra
1736:Properties
1050:References
610:such that
443:Properties
421:disk in a
398:is called
378:A disk in
347:disk in a
275:is called
70:is called
2951:Uniformly
2910:Reflexive
2758:Barrelled
2754:Countably
2666:Symmetric
2564:Transpose
2256:Countably
2246:Countably
2186:Operators
2177:Bornology
2143:bornology
1895:Unbounded
1890:Transpose
1848:Operators
1777:Separable
1772:Reflexive
1757:Algebraic
1743:Barrelled
1617:849801114
1587:840278135
1553:144216834
1448:840293704
1420:(1983) .
1383:316549583
1222:(1987) .
1212:878109401
1185:297140003
1028:Bornology
918:−
903:−
894:−
767:−
627:∩
512:⊆
449:absorbing
419:absorbing
345:absorbing
287:bornivore
76:bornivore
3010:Category
2995:Category
2946:Strictly
2920:Schwartz
2860:LF-space
2855:LB-space
2813:FK-space
2783:Complete
2763:BK-space
2688:Relative
2635:(subset)
2627:(subset)
2554:Seminorm
2537:Bilinear
2097:Category
1909:Algebras
1791:Theorems
1748:Complete
1717:Schwartz
1663:glossary
1597:(2013).
1526:37141279
1497:(1997).
1355:(1977).
1321:(1973).
1311:30593138
1284:21195908
1256:(1990).
1246:17499190
1001:See also
461:Suppose
451:. In a
2960:)
2908:)
2850:K-space
2835:Hilbert
2818:Fréchet
2803:F-space
2778:Brauner
2771:)
2756:)
2738:Asplund
2720:)
2690:)
2610:Bounded
2505:Compact
2490:Bounded
2427: (
2212:Subsets
1900:Unitary
1880:Nuclear
1865:Compact
1860:Bounded
1855:Adjoint
1829:Min–max
1722:Sobolev
1707:Nuclear
1697:Hilbert
1692:Fréchet
1657: (
1483:8588370
1440:0248498
1410:8210342
1375:0500064
408:absorbs
312:absorbs
80:absorbs
2972:Webbed
2958:Quasi-
2880:Montel
2870:Mackey
2769:Ultra-
2748:Banach
2656:Radial
2620:Convex
2590:Affine
2532:Linear
2500:Closed
2324:(TVSs)
2271:Quasi-
2173:Vector
1875:Normal
1712:Orlicz
1702:Hölder
1682:Banach
1671:Spaces
1659:topics
1615:
1605:
1585:
1575:
1551:
1541:
1524:
1514:
1481:
1471:
1446:
1438:
1428:
1408:
1398:
1381:
1373:
1363:
1345:886098
1343:
1333:
1309:
1299:
1282:
1272:
1244:
1234:
1210:
1200:
1183:
1173:
410:every
406:if it
314:every
283:and a
78:if it
74:and a
2930:Smith
2915:Riesz
2906:Semi-
2718:Quasi
2712:Polar
1687:Besov
1504:(PDF)
977:then
823:then
129:is a
2549:Norm
2473:form
2461:Maps
2141:and
2035:(or
1753:Dual
1613:OCLC
1603:ISBN
1583:OCLC
1573:ISBN
1549:OCLC
1539:ISBN
1522:OCLC
1512:ISBN
1479:OCLC
1469:ISBN
1444:OCLC
1426:ISBN
1406:OCLC
1396:ISBN
1379:OCLC
1361:ISBN
1341:OCLC
1331:ISBN
1307:OCLC
1297:ISBN
1280:OCLC
1270:ISBN
1242:OCLC
1232:ISBN
1208:OCLC
1198:ISBN
1181:OCLC
1171:ISBN
945:and
791:and
687:Let
501:and
439:").
414:.
207:.
200:.
1569:GTM
707:be
659:If
590:in
530:If
417:An
343:An
318:of
291:if
255:of
215:If
173:is
153:of
109:If
19:In
3012::
2273:)
2258:)
2248:)
2194:Un
2175:)
1661:–
1611:.
1581:.
1567:.
1547:.
1520:.
1510:.
1493:;
1477:.
1467:.
1459:.
1442:.
1436:MR
1434:.
1404:.
1377:.
1371:MR
1369:.
1339:.
1305:.
1278:.
1268:.
1260:.
1240:.
1226:.
1206:.
1179:.
1169:.
1113:^
1058:^
2956:(
2941:B
2939:(
2899:(
2767:(
2752:(
2716:(
2686:(
2436:)
2314:e
2307:t
2300:v
2269:(
2254:(
2244:(
2196:)
2192:(
2171:(
2131:e
2124:t
2117:v
2039:)
1763:)
1759:/
1755:(
1665:)
1647:e
1640:t
1633:v
1619:.
1589:.
1555:.
1528:.
1485:.
1450:.
1412:.
1385:.
1347:.
1313:.
1286:.
1248:.
1214:.
1187:.
985:T
965:)
962:1
959:,
956:1
953:(
933:,
930:)
927:1
924:,
921:1
915:(
912:,
909:)
906:1
900:,
897:1
891:(
871:T
851:S
831:S
811:)
808:1
805:,
802:1
799:(
779:)
776:1
773:,
770:1
764:(
744:S
722:2
717:R
695:X
667:X
633:.
630:M
624:C
621:=
618:B
598:X
578:C
558:M
538:B
518:.
515:M
509:B
489:X
469:M
386:X
329:.
326:X
299:S
263:X
243:S
223:X
187:X
161:X
141:S
117:X
97:.
92:B
56:B
31:X
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