158:
1912:
63:
22:
228:
1183:
972:
864:
759:
791:
1801:
405:
654:
434:
246:
486:
824:
1176:
908:
187:
1027:
717:
627:
572:
457:
1464:
1004:
928:
888:
694:
674:
604:
548:
526:
506:
375:
355:
335:
1627:
1169:
1754:
1609:
1585:
73:
1144:
1394:
1221:
35:
1477:
1110:
1566:
1457:
1343:
282:
264:
209:
49:
1836:
1297:
1267:
1192:
131:
1481:
103:
88:
1632:
1282:
1136:
1042:
1688:
110:
1936:
1915:
1637:
1622:
1450:
1431:
1652:
1415:
1897:
1657:
1851:
1775:
1410:
1236:
117:
1892:
1708:
170:
1642:
1744:
1545:
1338:
1231:
180:
174:
166:
41:
1617:
937:
866:
is countably order complete (that is, each subset that is bounded above has a supremum) but in general is not
829:
724:
99:
1841:
1211:
1872:
1816:
1780:
191:
764:
1855:
1363:
1206:
1821:
1759:
1473:
307:
384:
1846:
1713:
1128:
1277:
632:
124:
1826:
1389:
1307:
1150:
1140:
1116:
1106:
410:
462:
1831:
1749:
1718:
1698:
1683:
1678:
1673:
1510:
1333:
1292:
1262:
1257:
799:
1693:
1647:
1595:
1590:
1561:
1442:
1373:
893:
1520:
1009:
699:
609:
554:
439:
1882:
1734:
1535:
1353:
1348:
1328:
1302:
1287:
1272:
1241:
1047:
989:
913:
873:
867:
679:
659:
589:
533:
511:
491:
360:
340:
320:
315:
296:
1930:
1887:
1811:
1540:
1525:
1515:
1161:
1877:
1530:
1500:
1139:. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer.
303:
1806:
1796:
1703:
1505:
1216:
80:
62:
1739:
1579:
1575:
1571:
1358:
1226:
1154:
1120:
1105:. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press.
1368:
1037:
931:
378:
794:
1073:
1071:
1069:
1067:
986:
The intersection of an arbitrary family of bands in a vector lattice
1446:
1165:
221:
151:
56:
15:
793:) is the usual space of real valued functions used to define
1050: – Partially ordered vector space, ordered as a lattice
944:
836:
731:
1052:
Pages displaying short descriptions of redirect targets
242:
84:
1012:
992:
940:
916:
896:
876:
832:
802:
767:
727:
702:
682:
662:
635:
612:
592:
557:
536:
514:
494:
465:
442:
413:
387:
363:
343:
323:
1865:
1789:
1768:
1727:
1666:
1608:
1554:
1489:
1424:
1403:
1382:
1316:
1250:
1199:
237:
may be too technical for most readers to understand
1802:Spectral theory of ordinary differential equations
1021:
998:
966:
922:
902:
882:
858:
818:
785:
753:
711:
688:
668:
648:
621:
598:
566:
542:
520:
500:
480:
451:
428:
399:
369:
349:
329:
1077:
574:A band generated by a singleton set is called a
420:
179:but its sources remain unclear because it lacks
1101:Narici, Lawrence; Beckenstein, Edward (2011).
1458:
1177:
1089:
8:
89:introducing citations to additional sources
50:Learn how and when to remove these messages
1493:
1465:
1451:
1443:
1184:
1170:
1162:
1011:
991:
949:
943:
942:
939:
915:
895:
875:
841:
835:
834:
831:
807:
801:
766:
736:
730:
729:
726:
701:
681:
661:
640:
634:
611:
591:
556:
535:
513:
493:
464:
441:
412:
386:
362:
342:
322:
283:Learn how and when to remove this message
265:Learn how and when to remove this message
249:, without removing the technical details.
210:Learn how and when to remove this message
1755:Group algebra of a locally compact group
967:{\displaystyle {\mathcal {L}}^{p}(\mu )}
859:{\displaystyle {\mathcal {L}}^{p}(\mu )}
754:{\displaystyle {\mathcal {L}}^{p}(\mu )}
79:Relevant discussion may be found on the
1063:
488:The smallest band containing a subset
247:make it understandable to non-experts
7:
786:{\displaystyle 1\leq p\leq \infty }
780:
14:
1193:Ordered topological vector spaces
31:This article has multiple issues.
1911:
1910:
1837:Topological quantum field theory
302:In mathematics, specifically in
226:
156:
72:relies largely or entirely on a
61:
20:
39:or discuss these issues on the
961:
955:
890:is the vector subspace of all
853:
847:
748:
742:
1:
1633:Uniform boundedness principle
1283:Locally convex vector lattice
1078:Narici & Beckenstein 2011
1043:Locally convex vector lattice
1131:; Wolff, Manfred P. (1999).
400:{\displaystyle S\subseteq M}
1953:
1776:Invariant subspace problem
1237:Topological vector lattice
649:{\displaystyle S^{\perp }}
294:
1906:
1496:
1317:Types of elements/subsets
1133:Topological Vector Spaces
1103:Topological Vector Spaces
1090:Schaefer & Wolff 1999
1745:Spectrum of a C*-algebra
1232:Positive linear operator
429:{\displaystyle x=\sup S}
295:Not to be confused with
165:This article includes a
100:"Band" order theory
1842:Noncommutative geometry
1212:Partially ordered space
481:{\displaystyle x\in M.}
194:more precise citations.
1898:Tomita–Takesaki theory
1873:Approximation property
1817:Calculus of variations
1383:Topologies/Convergence
1251:Types of orders/spaces
1023:
1000:
968:
924:
904:
884:
860:
820:
819:{\displaystyle L^{p},}
787:
755:
713:
690:
670:
650:
623:
600:
568:
544:
522:
502:
482:
453:
430:
401:
381:and such that for all
371:
351:
331:
1893:Banach–Mazur distance
1856:Generalized functions
1024:
1001:
969:
925:
910:-null functions then
905:
885:
861:
821:
788:
756:
714:
691:
671:
651:
624:
601:
569:
545:
523:
503:
483:
454:
431:
402:
372:
352:
332:
1638:Kakutani fixed-point
1623:Riesz representation
1432:Freudenthal spectral
1364:Quasi-interior point
1207:Ordered vector space
1010:
990:
938:
914:
903:{\displaystyle \mu }
894:
874:
830:
800:
765:
725:
700:
680:
660:
633:
610:
606:of a vector lattice
590:
555:
534:
512:
492:
463:
440:
411:
385:
361:
341:
321:
85:improve this article
1937:Functional analysis
1822:Functional calculus
1781:Mahler's conjecture
1760:Von Neumann algebra
1474:Functional analysis
1129:Schaefer, Helmut H.
1092:, pp. 204–214.
1080:, pp. 204–214.
656:of all elements of
308:functional analysis
1847:Riemann hypothesis
1546:Topological vector
1022:{\displaystyle X.}
1019:
996:
964:
920:
900:
880:
856:
816:
783:
751:
712:{\displaystyle X.}
709:
686:
666:
646:
622:{\displaystyle X,}
619:
596:
567:{\displaystyle X.}
564:
540:
530:band generated by
518:
498:
478:
452:{\displaystyle X,}
449:
426:
397:
367:
347:
327:
167:list of references
1924:
1923:
1827:Integral operator
1604:
1603:
1440:
1439:
1390:Order convergence
1308:Regularly ordered
1146:978-1-4612-7155-0
999:{\displaystyle X}
923:{\displaystyle N}
883:{\displaystyle N}
689:{\displaystyle S}
669:{\displaystyle X}
599:{\displaystyle S}
543:{\displaystyle S}
521:{\displaystyle X}
501:{\displaystyle S}
370:{\displaystyle X}
350:{\displaystyle M}
330:{\displaystyle X}
293:
292:
285:
275:
274:
267:
220:
219:
212:
150:
149:
135:
54:
1944:
1914:
1913:
1832:Jones polynomial
1750:Operator algebra
1494:
1467:
1460:
1453:
1444:
1334:Lattice disjoint
1293:Order bound dual
1186:
1179:
1172:
1163:
1158:
1124:
1093:
1087:
1081:
1075:
1053:
1028:
1026:
1025:
1020:
1005:
1003:
1002:
997:
973:
971:
970:
965:
954:
953:
948:
947:
929:
927:
926:
921:
909:
907:
906:
901:
889:
887:
886:
881:
865:
863:
862:
857:
846:
845:
840:
839:
825:
823:
822:
817:
812:
811:
792:
790:
789:
784:
760:
758:
757:
752:
741:
740:
735:
734:
718:
716:
715:
710:
695:
693:
692:
687:
675:
673:
672:
667:
655:
653:
652:
647:
645:
644:
628:
626:
625:
620:
605:
603:
602:
597:
573:
571:
570:
565:
549:
547:
546:
541:
527:
525:
524:
519:
507:
505:
504:
499:
487:
485:
484:
479:
458:
456:
455:
450:
435:
433:
432:
427:
406:
404:
403:
398:
376:
374:
373:
368:
356:
354:
353:
348:
336:
334:
333:
328:
288:
281:
270:
263:
259:
256:
250:
230:
229:
222:
215:
208:
204:
201:
195:
190:this article by
181:inline citations
160:
159:
152:
145:
142:
136:
134:
93:
65:
57:
46:
24:
23:
16:
1952:
1951:
1947:
1946:
1945:
1943:
1942:
1941:
1927:
1926:
1925:
1920:
1902:
1866:Advanced topics
1861:
1785:
1764:
1723:
1689:Hilbert–Schmidt
1662:
1653:Gelfand–Naimark
1600:
1550:
1485:
1471:
1441:
1436:
1420:
1399:
1378:
1374:Weak order unit
1339:Dual/Polar cone
1312:
1278:Fréchet lattice
1246:
1195:
1190:
1147:
1127:
1113:
1100:
1097:
1096:
1088:
1084:
1076:
1065:
1060:
1051:
1034:
1008:
1007:
988:
987:
984:
941:
936:
935:
912:
911:
892:
891:
872:
871:
833:
828:
827:
803:
798:
797:
763:
762:
728:
723:
722:
698:
697:
678:
677:
658:
657:
636:
631:
630:
608:
607:
588:
587:
586:For any subset
584:
553:
552:
532:
531:
510:
509:
490:
489:
461:
460:
438:
437:
409:
408:
383:
382:
359:
358:
339:
338:
319:
318:
300:
289:
278:
277:
276:
271:
260:
254:
251:
243:help improve it
240:
231:
227:
216:
205:
199:
196:
185:
171:related reading
161:
157:
146:
140:
137:
94:
92:
78:
66:
25:
21:
12:
11:
5:
1950:
1948:
1940:
1939:
1929:
1928:
1922:
1921:
1919:
1918:
1907:
1904:
1903:
1901:
1900:
1895:
1890:
1885:
1883:Choquet theory
1880:
1875:
1869:
1867:
1863:
1862:
1860:
1859:
1849:
1844:
1839:
1834:
1829:
1824:
1819:
1814:
1809:
1804:
1799:
1793:
1791:
1787:
1786:
1784:
1783:
1778:
1772:
1770:
1766:
1765:
1763:
1762:
1757:
1752:
1747:
1742:
1737:
1735:Banach algebra
1731:
1729:
1725:
1724:
1722:
1721:
1716:
1711:
1706:
1701:
1696:
1691:
1686:
1681:
1676:
1670:
1668:
1664:
1663:
1661:
1660:
1658:Banach–Alaoglu
1655:
1650:
1645:
1640:
1635:
1630:
1625:
1620:
1614:
1612:
1606:
1605:
1602:
1601:
1599:
1598:
1593:
1588:
1586:Locally convex
1583:
1569:
1564:
1558:
1556:
1552:
1551:
1549:
1548:
1543:
1538:
1533:
1528:
1523:
1518:
1513:
1508:
1503:
1497:
1491:
1487:
1486:
1472:
1470:
1469:
1462:
1455:
1447:
1438:
1437:
1435:
1434:
1428:
1426:
1422:
1421:
1419:
1418:
1413:
1407:
1405:
1401:
1400:
1398:
1397:
1395:Order topology
1392:
1386:
1384:
1380:
1379:
1377:
1376:
1371:
1366:
1361:
1356:
1354:Order summable
1351:
1349:Order complete
1346:
1341:
1336:
1331:
1329:Cone-saturated
1326:
1320:
1318:
1314:
1313:
1311:
1310:
1305:
1303:Order complete
1300:
1295:
1290:
1288:Normed lattice
1285:
1280:
1275:
1273:Banach lattice
1270:
1265:
1260:
1254:
1252:
1248:
1247:
1245:
1244:
1242:Vector lattice
1239:
1234:
1229:
1224:
1222:Order topology
1219:
1214:
1209:
1203:
1201:
1200:Basic concepts
1197:
1196:
1191:
1189:
1188:
1181:
1174:
1166:
1160:
1159:
1145:
1125:
1112:978-1584888666
1111:
1095:
1094:
1082:
1062:
1061:
1059:
1056:
1055:
1054:
1048:Vector lattice
1045:
1040:
1033:
1030:
1018:
1015:
995:
983:
980:
977:
963:
960:
957:
952:
946:
919:
899:
879:
868:order complete
855:
852:
849:
844:
838:
815:
810:
806:
782:
779:
776:
773:
770:
750:
747:
744:
739:
733:
708:
705:
685:
676:disjoint from
665:
643:
639:
618:
615:
595:
583:
580:
576:principal band
563:
560:
539:
528:is called the
517:
497:
477:
474:
471:
468:
448:
445:
425:
422:
419:
416:
396:
393:
390:
366:
346:
337:is a subspace
326:
316:vector lattice
297:Band (algebra)
291:
290:
273:
272:
234:
232:
225:
218:
217:
200:September 2020
175:external links
164:
162:
155:
148:
147:
83:. Please help
69:
67:
60:
55:
29:
28:
26:
19:
13:
10:
9:
6:
4:
3:
2:
1949:
1938:
1935:
1934:
1932:
1917:
1909:
1908:
1905:
1899:
1896:
1894:
1891:
1889:
1888:Weak topology
1886:
1884:
1881:
1879:
1876:
1874:
1871:
1870:
1868:
1864:
1857:
1853:
1850:
1848:
1845:
1843:
1840:
1838:
1835:
1833:
1830:
1828:
1825:
1823:
1820:
1818:
1815:
1813:
1812:Index theorem
1810:
1808:
1805:
1803:
1800:
1798:
1795:
1794:
1792:
1788:
1782:
1779:
1777:
1774:
1773:
1771:
1769:Open problems
1767:
1761:
1758:
1756:
1753:
1751:
1748:
1746:
1743:
1741:
1738:
1736:
1733:
1732:
1730:
1726:
1720:
1717:
1715:
1712:
1710:
1707:
1705:
1702:
1700:
1697:
1695:
1692:
1690:
1687:
1685:
1682:
1680:
1677:
1675:
1672:
1671:
1669:
1665:
1659:
1656:
1654:
1651:
1649:
1646:
1644:
1641:
1639:
1636:
1634:
1631:
1629:
1626:
1624:
1621:
1619:
1616:
1615:
1613:
1611:
1607:
1597:
1594:
1592:
1589:
1587:
1584:
1581:
1577:
1573:
1570:
1568:
1565:
1563:
1560:
1559:
1557:
1553:
1547:
1544:
1542:
1539:
1537:
1534:
1532:
1529:
1527:
1524:
1522:
1519:
1517:
1514:
1512:
1509:
1507:
1504:
1502:
1499:
1498:
1495:
1492:
1488:
1483:
1479:
1475:
1468:
1463:
1461:
1456:
1454:
1449:
1448:
1445:
1433:
1430:
1429:
1427:
1423:
1417:
1414:
1412:
1409:
1408:
1406:
1402:
1396:
1393:
1391:
1388:
1387:
1385:
1381:
1375:
1372:
1370:
1367:
1365:
1362:
1360:
1357:
1355:
1352:
1350:
1347:
1345:
1342:
1340:
1337:
1335:
1332:
1330:
1327:
1325:
1322:
1321:
1319:
1315:
1309:
1306:
1304:
1301:
1299:
1296:
1294:
1291:
1289:
1286:
1284:
1281:
1279:
1276:
1274:
1271:
1269:
1266:
1264:
1261:
1259:
1256:
1255:
1253:
1249:
1243:
1240:
1238:
1235:
1233:
1230:
1228:
1225:
1223:
1220:
1218:
1215:
1213:
1210:
1208:
1205:
1204:
1202:
1198:
1194:
1187:
1182:
1180:
1175:
1173:
1168:
1167:
1164:
1156:
1152:
1148:
1142:
1138:
1134:
1130:
1126:
1122:
1118:
1114:
1108:
1104:
1099:
1098:
1091:
1086:
1083:
1079:
1074:
1072:
1070:
1068:
1064:
1057:
1049:
1046:
1044:
1041:
1039:
1036:
1035:
1031:
1029:
1016:
1013:
1006:is a band in
993:
981:
979:
975:
958:
950:
933:
917:
897:
877:
869:
850:
842:
813:
808:
804:
796:
777:
774:
771:
768:
745:
737:
719:
706:
703:
696:is a band in
683:
663:
641:
637:
616:
613:
593:
581:
579:
577:
561:
558:
550:
537:
515:
495:
475:
472:
469:
466:
446:
443:
423:
417:
414:
394:
391:
388:
380:
364:
344:
324:
317:
313:
309:
305:
298:
287:
284:
269:
266:
258:
248:
244:
238:
235:This article
233:
224:
223:
214:
211:
203:
193:
189:
183:
182:
176:
172:
168:
163:
154:
153:
144:
133:
130:
126:
123:
119:
116:
112:
109:
105:
102: –
101:
97:
96:Find sources:
90:
86:
82:
76:
75:
74:single source
70:This article
68:
64:
59:
58:
53:
51:
44:
43:
38:
37:
32:
27:
18:
17:
1878:Balanced set
1852:Distribution
1790:Applications
1643:Krein–Milman
1628:Closed graph
1425:Main results
1323:
1132:
1102:
1085:
985:
932:solid subset
720:
585:
575:
529:
311:
304:order theory
301:
279:
261:
252:
236:
206:
197:
186:Please help
178:
138:
128:
121:
114:
107:
95:
71:
47:
40:
34:
33:Please help
30:
1807:Heat kernel
1797:Hardy space
1704:Trace class
1618:Hahn–Banach
1580:Topological
1344:Normal cone
1268:Archimedean
1217:Riesz space
192:introducing
1740:C*-algebra
1555:Properties
1359:Order unit
1298:Order dual
1227:Order unit
1058:References
982:Properties
436:exists in
407:such that
111:newspapers
36:improve it
1714:Unbounded
1709:Transpose
1667:Operators
1596:Separable
1591:Reflexive
1576:Algebraic
1562:Barrelled
1404:Operators
1369:Solid set
1155:840278135
1121:144216834
1038:Solid set
978:a band.
959:μ
898:μ
851:μ
795:Lp spaces
781:∞
778:≤
772:≤
746:μ
642:⊥
470:∈
392:⊆
255:June 2020
141:June 2020
81:talk page
42:talk page
1931:Category
1916:Category
1728:Algebras
1610:Theorems
1567:Complete
1536:Schwartz
1482:glossary
1411:Positive
1263:AM-space
1258:AL-space
1032:See also
974:that is
629:the set
582:Examples
459:we have
377:that is
1719:Unitary
1699:Nuclear
1684:Compact
1679:Bounded
1674:Adjoint
1648:Min–max
1541:Sobolev
1526:Nuclear
1516:Hilbert
1511:Fréchet
1476: (
241:Please
188:improve
125:scholar
1694:Normal
1531:Orlicz
1521:Hölder
1501:Banach
1490:Spaces
1478:topics
1153:
1143:
1119:
1109:
870:. If
127:
120:
113:
106:
98:
1506:Besov
1416:State
930:is a
826:then
379:solid
314:in a
173:, or
132:JSTOR
118:books
1854:(or
1572:Dual
1324:Band
1151:OCLC
1141:ISBN
1117:OCLC
1107:ISBN
312:band
310:, a
306:and
104:news
1137:GTM
976:not
934:of
721:If
578:.
551:in
508:of
421:sup
357:of
245:to
87:by
1933::
1480:–
1149:.
1135:.
1115:.
1066:^
177:,
169:,
45:.
1858:)
1582:)
1578:/
1574:(
1484:)
1466:e
1459:t
1452:v
1185:e
1178:t
1171:v
1157:.
1123:.
1017:.
1014:X
994:X
962:)
956:(
951:p
945:L
918:N
878:N
854:)
848:(
843:p
837:L
814:,
809:p
805:L
775:p
769:1
761:(
749:)
743:(
738:p
732:L
707:.
704:X
684:S
664:X
638:S
617:,
614:X
594:S
562:.
559:X
538:S
516:X
496:S
476:.
473:M
467:x
447:,
444:X
424:S
418:=
415:x
395:M
389:S
365:X
345:M
325:X
299:.
286:)
280:(
268:)
262:(
257:)
253:(
239:.
213:)
207:(
202:)
198:(
184:.
143:)
139:(
129:·
122:·
115:·
108:·
91:.
77:.
52:)
48:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
