2237:
743:
A more thorough discussion of the origins of the Orlicz–Pettis theorem and, in particular, of the paper can be found in. See also footnote 5 on p. 839 of and the comments at the end of
Section 2.4 of the 2nd edition of the quoted book by Albiac and Kalton. Though in Polish, there is also an
727:
was only used to guarantee the existence of the weak limits of the considered series. Consequently, assuming the existence of those limits, which amounts to the assumption of the weak subseries convergence of the series, the same proof shows that the series in norm convergent. In other words, the
755:
proved a theorem, whose special case is the Orlicz–Pettis theorem in locally convex spaces. Later, a more direct proofs of the form (i) of the theorem in the locally convex case were provided by McArthur and
Robertson.
764:
The theorem of Orlicz and Pettis had been strengthened and generalized in many directions. An early survey of this area of research is Kalton's paper. A natural setting for subseries convergence is that of an
642:
217:
975:
562:
272:
135:
1136:(in the original statement of the Andersen-Christensen theorem the assumption of sequential completeness is missing), which in turn extends the corresponding theorem of Kalton for a
483:
The history of the origins of the theorem is somewhat complicated. In numerous papers and books there are misquotations or/and misconceptions concerning the result. Assuming that
433:
919:
1257:
354:
1168:
841:
682:
379:
1718:
1134:
1050:
893:
736:
directly referred to Orlicz's theorem in Banach's book. Needing the result in order to show the coincidence of the weak and strong measures, he provided a proof. Also
1078:
995:
399:
1098:
1015:
1215:
84:
457:
1277:
1188:
861:
815:
789:
725:
702:
501:
477:
312:
292:
159:
53:
728:
version (i) of the Orlicz–Pettis theorem holds. The theorem in this form, openly credited to Orlicz, appeared in Banach's monograph in the last chapter
2126:
1053:
1723:
1657:
1566:
1962:
1789:
1674:
1652:
1561:
1346:
1326:
1952:
567:
2261:
2079:
1934:
1910:
791:
and a representative result of this area of research is the following theorem, called by Kalton the Graves-Labuda-Pachl
Theorem.
56:
1802:
1605:
1891:
1782:
1757:
707:
After the paper was published, Orlicz realized that in the proof of the theorem the weak sequential completeness of
164:
1388:
2161:
1806:
1441:
924:
516:
226:
89:
1316:
Théorie des opérations linéaires, Monografje matematyczne, Warszawa 1932; Oeuvres. Vol. II}, PWN, Warszawa 1979.
1463:
1957:
1635:
1588:
404:
2240:
2013:
1947:
1775:
898:
1419:
1977:
1584:
Some results on Borel structures with applications to subseries convergence in
Abelian topological groups
2222:
2176:
2100:
1982:
1220:
317:
2217:
2033:
1541:
1521:
1146:
820:
647:
2069:
1967:
1870:
459:
is weakly countably additive, then it is countably additive (in the original topology of the space
362:
2166:
1942:
1678:
1433:
1143:
The limitations for this kind of results are provided by the weak* topology of the Banach space
1107:
1023:
866:
2197:
2141:
2105:
1630:
1610:
1583:
1393:
752:
1904:
1259:) subseries convergence does not imply the subseries convergence in the F-norm of the space
1063:
980:
504:
436:
384:
29:
1900:
1501:
1083:
1000:
2180:
1562:
Universal Lusin measurability and subfamily summable families in
Abelian topological groups
1193:
62:
25:
1767:
442:
8:
2146:
2084:
1798:
17:
2171:
2038:
1371:
1300:
1262:
1173:
846:
800:
774:
745:
733:
710:
687:
486:
462:
297:
277:
144:
38:
1458:
2151:
1753:
1366:
1295:
769:
21:
2156:
2074:
2043:
2023:
2008:
2003:
1998:
1409:
W. Orlicz, Collected works, Vol.1, PWN-Polish
Scientific Publishers, Warszawa 1988.
1835:
740:
gave a proof (with a remark that it is similar to the original proof of Orlicz).
2018:
1972:
1920:
1915:
1886:
1845:
2207:
2059:
1860:
1101:
1100:. This is a generalization of an analogical result for a sequentially complete
977:
is universally measurable. Then the subseries convergence for both topologies
737:
2255:
2212:
2136:
1865:
1850:
1840:
766:
1480:
2202:
1855:
1825:
1626:
1137:
1522:
Universal measurability and summable families in topological vector spaces
2131:
2121:
2028:
1830:
2064:
1896:
1434:
Sur les applications linéaires faiblement compacts d'espaces du type
1631:
Subseries convergence in topological groups and vector measures
637:{\displaystyle \sum _{n=1}^{\infty }|x^{*}(x_{n})|<\infty }
1653:
On the Orlicz-Pettis property in non-locally convex F-spaces
1797:
748:, Orlicz’s first PhD-student, still in the occupied Lwów.
1675:
The Orlicz-Pettis theorem fails for Lumer's Hardy spaces
1481:
On unconditional convergence in topological vector spaces
1389:
Essays on the Orlicz-Petts theorem, I (The two theorems)
744:
adequate comment on page 284 of the quoted monograph of
1140:
group, a theorem that triggered this series of papers.
1420:"Władysław Orlicz - the Mathematics Genealogy Project"
1056:
group, then the conclusion of the theorem is true for
1681:
1265:
1223:
1196:
1176:
1149:
1110:
1086:
1066:
1026:
1003:
983:
927:
901:
869:
849:
823:
803:
777:
713:
690:
650:
570:
519:
489:
465:
445:
407:
387:
365:
320:
300:
280:
229:
219:
are convergent. The theorem says that, equivalently,
167:
147:
92:
65:
41:
1367:
Beiträge zur
Theorie der Orthogonalentwicklungen II
1296:
Beiträge zur
Theorie der Orthogonalentwicklungen II
2127:Spectral theory of ordinary differential equations
1712:
1271:
1251:
1209:
1182:
1162:
1128:
1092:
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1009:
989:
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855:
835:
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783:
719:
696:
676:
636:
556:
495:
471:
451:
427:
393:
373:
348:
306:
286:
266:
211:
153:
129:
78:
47:
2253:
1724:Proceedings of the American Mathematical Society
1658:Proceedings of the American Mathematical Society
1567:Proceedings of the American Mathematical Society
212:{\displaystyle \sum _{k=1}^{\infty }~x_{n_{k}}}
759:
503:is weakly sequentially complete Banach space,
1783:
1747:
1582:N. J. M. Andersen and J. P. R. Christensen,
970:{\displaystyle j:(X,\alpha )\to (X,\beta )}
684:, then the series is (norm) convergent in
557:{\displaystyle \sum _{n=1}^{\infty }~x_{n}}
267:{\displaystyle \sum _{n=1}^{\infty }~x_{n}}
130:{\displaystyle \sum _{n=1}^{\infty }~x_{n}}
1790:
1776:
1742:. Państwowe Wydawnictwo Naukowe, Warszawa.
1737:
32:(Pettis) with values in abstract spaces.
2080:Group algebra of a locally compact group
1748:Albiac, Fernando; Kalton, Nigel (2016).
564:is weakly unconditionally Cauchy, i.e.,
356:), then it is (subseries) convergent; or
1606:Measure, Category and Convergent Series
57:locally convex topological vector space
2254:
428:{\displaystyle \mu :\mathbf {A} \to X}
1771:
1750:Topics in Banach space theory, 2nd ed
914:{\displaystyle \alpha \subset \beta }
1542:A note on the Orlicz-Pettis Theorem
294:(i.e., is subseries convergent in
13:
1155:
843:two Hausdorff group topologies on
732:in which no proofs were provided.
631:
587:
536:
314:with respect to its weak topology
274:is weakly subseries convergent in
246:
184:
109:
14:
2273:
1546:Indagationes Mathematicae (N. S.)
1526:Indagationes Mathematicae (N. S.)
1459:On a theorem of Orlicz and Pettis
2236:
2235:
2162:Topological quantum field theory
1252:{\displaystyle \sigma (X,X^{*})}
415:
367:
349:{\displaystyle \sigma (X,X^{*})}
2262:Theorems in functional analysis
1667:
1645:
1620:
1598:
1576:
1554:
1534:
1514:
1494:
1473:
1451:
1442:Canadian Journal of Mathematics
1327:On integration in vector spaces
1163:{\displaystyle \ell ^{\infty }}
1707:
1701:
1692:
1682:
1464:Pacific Journal of Mathematics
1426:
1412:
1403:
1381:
1359:
1339:
1319:
1310:
1288:
1246:
1227:
1123:
1111:
1039:
1027:
964:
952:
949:
946:
934:
882:
870:
836:{\displaystyle \alpha ,\beta }
677:{\displaystyle x^{*}\in X^{*}}
624:
620:
607:
593:
419:
343:
324:
1:
1958:Uniform boundedness principle
1636:Israel Journal of Mathematics
1589:Israel Journal of Mathematics
1282:
1170:and the examples of F-spaces
1738:Alexiewicz, Andrzej (1969).
644:for each linear functional
374:{\displaystyle \mathbf {A} }
7:
1713:{\displaystyle (LH)^{p}(B)}
1485:Proc. Roy. Soc. Edinburgh A
1347:Uniformity in linear spaces
1217:such that the weak (i.e.,
1052:is a sequentially complete
760:Orlicz-Pettis type theorems
24:(Orlicz) or, equivalently,
10:
2278:
2101:Invariant subspace problem
1387:W. Filter and I. Labuda,
1129:{\displaystyle (X,\beta )}
1045:{\displaystyle (X,\beta )}
895:is sequentially complete,
888:{\displaystyle (X,\beta )}
2231:
2190:
2114:
2093:
2052:
1991:
1933:
1879:
1821:
1814:
1502:The Orlicz-Pettis theorem
1060:Hausdorff group topology
401:-algebra of sets and let
2070:Spectrum of a C*-algebra
1506:Contemporary Mathematics
817:be an Abelian group and
161:), if all its subseries
2167:Noncommutative geometry
1351:Trans. Amer. Math. Soc.
1331:Trans. Amer. Math. Soc.
1073:{\displaystyle \alpha }
990:{\displaystyle \alpha }
394:{\displaystyle \sigma }
2223:Tomita–Takesaki theory
2198:Approximation property
2142:Calculus of variations
1714:
1394:Real Analysis Exchange
1273:
1253:
1211:
1184:
1164:
1130:
1094:
1093:{\displaystyle \beta }
1074:
1046:
1011:
1010:{\displaystyle \beta }
991:
971:
915:
889:
857:
837:
811:
785:
721:
698:
678:
638:
591:
558:
540:
497:
473:
453:
429:
395:
375:
350:
308:
288:
268:
250:
213:
188:
155:
131:
113:
80:
49:
2218:Banach–Mazur distance
2181:Generalized functions
1715:
1274:
1254:
1212:
1210:{\displaystyle X^{*}}
1190:with separating dual
1185:
1165:
1131:
1095:
1075:
1047:
1020:As a consequence, if
1012:
992:
972:
916:
890:
858:
838:
812:
786:
722:
699:
679:
639:
571:
559:
520:
507:proved the following
498:
474:
454:
437:additive set function
430:
396:
376:
351:
309:
289:
269:
230:
214:
168:
156:
132:
93:
81:
79:{\displaystyle X^{*}}
50:
1963:Kakutani fixed-point
1948:Riesz representation
1740:Analiza Funkcjonalna
1679:
1400:, 1990-91, 393--403.
1263:
1221:
1194:
1174:
1147:
1108:
1084:
1064:
1024:
1001:
981:
925:
899:
867:
847:
821:
801:
775:
711:
688:
648:
568:
517:
487:
463:
452:{\displaystyle \mu }
443:
405:
385:
363:
318:
298:
278:
227:
165:
145:
139:subseries convergent
90:
63:
39:
26:countable additivity
2147:Functional calculus
2106:Mahler's conjecture
2085:Von Neumann algebra
1799:Functional analysis
1611:Real Anal. Exchange
921:, and the identity
18:functional analysis
2172:Riemann hypothesis
1871:Topological vector
1710:
1664:(1987), 492--–496.
1372:Studia Mathematica
1301:Studia Mathematica
1269:
1249:
1207:
1180:
1160:
1126:
1090:
1070:
1042:
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987:
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911:
885:
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833:
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694:
674:
634:
554:
493:
469:
449:
425:
391:
371:
346:
304:
284:
264:
209:
151:
127:
76:
45:
2249:
2248:
2152:Integral operator
1929:
1928:
1617:(2017), 411--428.
1595:(1973), 414--420.
1491:(1969), 145--157.
1479:A.P. Robertson,
1470:(1967), 297--302.
1448:(1953), 129--173.
1378:(1929), 241–255.
1307:(1929), 241–255.
1272:{\displaystyle X}
1183:{\displaystyle X}
856:{\displaystyle X}
810:{\displaystyle X}
784:{\displaystyle X}
770:topological group
720:{\displaystyle X}
697:{\displaystyle X}
543:
496:{\displaystyle X}
472:{\displaystyle X}
307:{\displaystyle X}
287:{\displaystyle X}
253:
191:
154:{\displaystyle X}
116:
48:{\displaystyle X}
22:convergent series
2269:
2239:
2238:
2157:Jones polynomial
2075:Operator algebra
1819:
1818:
1792:
1785:
1778:
1769:
1768:
1763:
1743:
1731:
1730:(1990), 957–963.
1719:
1717:
1716:
1711:
1700:
1699:
1671:
1665:
1649:
1643:
1642:(1971), 402-412.
1624:
1618:
1602:
1596:
1580:
1574:
1558:
1552:
1538:
1532:
1518:
1512:
1498:
1492:
1477:
1471:
1455:
1449:
1432:A.Grothendieck,
1430:
1424:
1423:
1416:
1410:
1407:
1401:
1385:
1379:
1363:
1357:
1356:(1938), 305–356.
1343:
1337:
1336:(1938), 277–304.
1323:
1317:
1314:
1308:
1292:
1278:
1276:
1275:
1270:
1258:
1256:
1255:
1250:
1245:
1244:
1216:
1214:
1213:
1208:
1206:
1205:
1189:
1187:
1186:
1181:
1169:
1167:
1166:
1161:
1159:
1158:
1135:
1133:
1132:
1127:
1099:
1097:
1096:
1091:
1079:
1077:
1076:
1071:
1051:
1049:
1048:
1043:
1016:
1014:
1013:
1008:
996:
994:
993:
988:
976:
974:
973:
968:
920:
918:
917:
912:
894:
892:
891:
886:
862:
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839:
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790:
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619:
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563:
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541:
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342:
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310:
305:
293:
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271:
270:
265:
263:
262:
251:
249:
244:
223:(i) If a series
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205:
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182:
160:
158:
157:
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136:
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125:
114:
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107:
85:
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82:
77:
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74:
54:
52:
51:
46:
2277:
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2252:
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2250:
2245:
2227:
2191:Advanced topics
2186:
2110:
2089:
2048:
2014:Hilbert–Schmidt
1987:
1978:Gelfand–Naimark
1925:
1875:
1810:
1796:
1760:
1734:
1695:
1691:
1680:
1677:
1676:
1672:
1668:
1650:
1646:
1625:
1621:
1603:
1599:
1581:
1577:
1573:(1979), 45--50.
1559:
1555:
1539:
1535:
1519:
1515:
1511:(1980), 91–100.
1499:
1495:
1478:
1474:
1456:
1452:
1431:
1427:
1418:
1417:
1413:
1408:
1404:
1386:
1382:
1364:
1360:
1344:
1340:
1324:
1320:
1315:
1311:
1293:
1289:
1285:
1264:
1261:
1260:
1240:
1236:
1222:
1219:
1218:
1201:
1197:
1195:
1192:
1191:
1175:
1172:
1171:
1154:
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1145:
1144:
1109:
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982:
979:
978:
926:
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900:
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896:
868:
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848:
845:
844:
822:
819:
818:
802:
799:
798:
776:
773:
772:
762:
712:
709:
708:
689:
686:
685:
668:
664:
655:
651:
649:
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645:
623:
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586:
575:
569:
566:
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548:
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518:
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514:
488:
485:
484:
464:
461:
460:
444:
441:
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414:
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403:
402:
386:
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382:
366:
364:
361:
360:
337:
333:
319:
316:
315:
299:
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295:
279:
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258:
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234:
228:
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201:
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162:
146:
143:
142:
121:
117:
108:
97:
91:
88:
87:
70:
66:
64:
61:
60:
55:be a Hausdorff
40:
37:
36:
12:
11:
5:
2275:
2265:
2264:
2247:
2246:
2244:
2243:
2232:
2229:
2228:
2226:
2225:
2220:
2215:
2210:
2208:Choquet theory
2205:
2200:
2194:
2192:
2188:
2187:
2185:
2184:
2174:
2169:
2164:
2159:
2154:
2149:
2144:
2139:
2134:
2129:
2124:
2118:
2116:
2112:
2111:
2109:
2108:
2103:
2097:
2095:
2091:
2090:
2088:
2087:
2082:
2077:
2072:
2067:
2062:
2060:Banach algebra
2056:
2054:
2050:
2049:
2047:
2046:
2041:
2036:
2031:
2026:
2021:
2016:
2011:
2006:
2001:
1995:
1993:
1989:
1988:
1986:
1985:
1983:Banach–Alaoglu
1980:
1975:
1970:
1965:
1960:
1955:
1950:
1945:
1939:
1937:
1931:
1930:
1927:
1926:
1924:
1923:
1918:
1913:
1911:Locally convex
1908:
1894:
1889:
1883:
1881:
1877:
1876:
1874:
1873:
1868:
1863:
1858:
1853:
1848:
1843:
1838:
1833:
1828:
1822:
1816:
1812:
1811:
1795:
1794:
1787:
1780:
1772:
1766:
1765:
1758:
1745:
1733:
1732:
1709:
1706:
1703:
1698:
1694:
1690:
1687:
1684:
1666:
1644:
1619:
1597:
1575:
1560:W. H. Graves,
1553:
1550:(1979), 35-37.
1533:
1531:(1979), 27-34.
1513:
1500:Nigel Kalton,
1493:
1472:
1457:C.W. McArthur
1450:
1425:
1411:
1402:
1380:
1358:
1338:
1318:
1309:
1286:
1284:
1281:
1268:
1248:
1243:
1239:
1235:
1232:
1229:
1226:
1204:
1200:
1179:
1157:
1153:
1125:
1122:
1119:
1116:
1113:
1089:
1069:
1041:
1038:
1035:
1032:
1029:
1006:
986:
966:
963:
960:
957:
954:
951:
948:
945:
942:
939:
936:
933:
930:
910:
907:
904:
884:
881:
878:
875:
872:
852:
832:
829:
826:
806:
780:
761:
758:
716:
693:
671:
667:
663:
658:
654:
633:
630:
626:
622:
617:
613:
609:
604:
600:
595:
589:
584:
581:
578:
574:
551:
547:
538:
533:
530:
527:
523:
492:
481:
480:
468:
448:
424:
421:
417:
413:
410:
390:
369:
357:
345:
340:
336:
332:
329:
326:
323:
303:
283:
261:
257:
248:
243:
240:
237:
233:
204:
200:
195:
186:
181:
178:
175:
171:
150:
124:
120:
111:
106:
103:
100:
96:
73:
69:
44:
9:
6:
4:
3:
2:
2274:
2263:
2260:
2259:
2257:
2242:
2234:
2233:
2230:
2224:
2221:
2219:
2216:
2214:
2213:Weak topology
2211:
2209:
2206:
2204:
2201:
2199:
2196:
2195:
2193:
2189:
2182:
2178:
2175:
2173:
2170:
2168:
2165:
2163:
2160:
2158:
2155:
2153:
2150:
2148:
2145:
2143:
2140:
2138:
2137:Index theorem
2135:
2133:
2130:
2128:
2125:
2123:
2120:
2119:
2117:
2113:
2107:
2104:
2102:
2099:
2098:
2096:
2094:Open problems
2092:
2086:
2083:
2081:
2078:
2076:
2073:
2071:
2068:
2066:
2063:
2061:
2058:
2057:
2055:
2051:
2045:
2042:
2040:
2037:
2035:
2032:
2030:
2027:
2025:
2022:
2020:
2017:
2015:
2012:
2010:
2007:
2005:
2002:
2000:
1997:
1996:
1994:
1990:
1984:
1981:
1979:
1976:
1974:
1971:
1969:
1966:
1964:
1961:
1959:
1956:
1954:
1951:
1949:
1946:
1944:
1941:
1940:
1938:
1936:
1932:
1922:
1919:
1917:
1914:
1912:
1909:
1906:
1902:
1898:
1895:
1893:
1890:
1888:
1885:
1884:
1882:
1878:
1872:
1869:
1867:
1864:
1862:
1859:
1857:
1854:
1852:
1849:
1847:
1844:
1842:
1839:
1837:
1834:
1832:
1829:
1827:
1824:
1823:
1820:
1817:
1813:
1808:
1804:
1800:
1793:
1788:
1786:
1781:
1779:
1774:
1773:
1770:
1761:
1759:9783319315553
1755:
1751:
1746:
1741:
1736:
1735:
1729:
1726:
1725:
1720:
1704:
1696:
1688:
1685:
1673:M. Nawrocki,
1670:
1663:
1660:
1659:
1654:
1651:M. Nawrocki,
1648:
1641:
1638:
1637:
1632:
1628:
1623:
1616:
1613:
1612:
1607:
1601:
1594:
1591:
1590:
1585:
1579:
1572:
1569:
1568:
1563:
1557:
1551:
1549:
1543:
1540:J. K. Pachl,
1537:
1530:
1527:
1523:
1517:
1510:
1507:
1503:
1497:
1490:
1486:
1482:
1476:
1469:
1466:
1465:
1460:
1454:
1447:
1444:
1443:
1438:
1437:
1429:
1421:
1415:
1406:
1399:
1396:
1395:
1390:
1384:
1377:
1374:
1373:
1368:
1362:
1355:
1352:
1348:
1342:
1335:
1332:
1328:
1325:B.J. Pettis,
1322:
1313:
1306:
1303:
1302:
1297:
1291:
1287:
1280:
1266:
1241:
1237:
1233:
1230:
1224:
1202:
1198:
1177:
1151:
1141:
1139:
1120:
1117:
1114:
1103:
1087:
1067:
1059:
1055:
1036:
1033:
1030:
1018:
1017:is the same.
1004:
984:
961:
958:
955:
943:
940:
937:
931:
928:
908:
905:
902:
879:
876:
873:
850:
830:
827:
824:
804:
796:
792:
778:
771:
768:
757:
754:
749:
747:
741:
739:
735:
731:
714:
705:
691:
669:
665:
661:
656:
652:
628:
615:
611:
602:
598:
582:
579:
576:
572:
549:
545:
531:
528:
525:
521:
513:If a series
512:
508:
506:
490:
466:
446:
438:
422:
411:
408:
388:
358:
338:
334:
330:
327:
321:
301:
281:
259:
255:
241:
238:
235:
231:
222:
221:
220:
202:
198:
193:
179:
176:
173:
169:
148:
140:
122:
118:
104:
101:
98:
94:
71:
67:
58:
42:
33:
31:
27:
23:
19:
16:A theorem in
2203:Balanced set
2177:Distribution
2115:Applications
1968:Krein–Milman
1953:Closed graph
1752:. Springer.
1749:
1739:
1727:
1722:
1669:
1661:
1656:
1647:
1639:
1634:
1627:N. J. Kalton
1622:
1614:
1609:
1600:
1592:
1587:
1578:
1570:
1565:
1556:
1547:
1545:
1536:
1528:
1525:
1520:Iwo Labuda,
1516:
1508:
1505:
1496:
1488:
1484:
1475:
1467:
1462:
1453:
1445:
1440:
1435:
1428:
1414:
1405:
1397:
1392:
1383:
1375:
1370:
1361:
1353:
1350:
1345:N. Dunford,
1341:
1333:
1330:
1321:
1312:
1304:
1299:
1290:
1142:
1080:weaker than
1057:
1019:
794:
793:
763:
753:Grothendieck
750:
742:
729:
706:
510:
509:
482:
138:
86:. A series
34:
15:
2132:Heat kernel
2122:Hardy space
2029:Trace class
1943:Hahn–Banach
1905:Topological
1604:I. Labuda,
1365:W. Orlicz,
1294:W. Orlicz,
20:concerning
2065:C*-algebra
1880:Properties
1283:References
1054:K-analytic
863:such that
746:Alexiewicz
59:with dual
2039:Unbounded
2034:Transpose
1992:Operators
1921:Separable
1916:Reflexive
1901:Algebraic
1887:Barrelled
1242:∗
1225:σ
1203:∗
1156:∞
1152:ℓ
1121:β
1088:β
1068:α
1037:β
1005:β
985:α
962:β
950:→
944:α
909:β
906:⊂
903:α
880:β
831:β
825:α
730:Remarques
670:∗
662:∈
657:∗
632:∞
603:∗
588:∞
573:∑
537:∞
522:∑
505:W. Orlicz
447:μ
420:→
409:μ
389:σ
359:(ii) Let
339:∗
322:σ
247:∞
232:∑
185:∞
170:∑
110:∞
95:∑
72:∗
2256:Category
2241:Category
2053:Algebras
1935:Theorems
1892:Complete
1861:Schwartz
1807:glossary
1102:analytic
795:Theorem.
511:Theorem.
30:measures
2044:Unitary
2024:Nuclear
2009:Compact
2004:Bounded
1999:Adjoint
1973:Min–max
1866:Sobolev
1851:Nuclear
1841:Hilbert
1836:Fréchet
1801: (
1104:group
767:Abelian
738:Dunford
2019:Normal
1856:Orlicz
1846:Hölder
1826:Banach
1815:Spaces
1803:topics
1756:
1138:Polish
734:Pettis
542:
435:be an
252:
190:
115:
1831:Besov
1615:32(2)
1398:16(2)
1058:every
439:. If
381:be a
2179:(or
1897:Dual
1754:ISBN
1436:C(K)
997:and
797:Let
629:<
141:(in
137:is
35:Let
1728:109
1662:101
1483:,
751:In
28:of
2258::
1805:–
1721:,
1655:,
1640:10
1633:,
1629:,
1608:,
1593:15
1586:,
1571:73
1564:,
1548:82
1544:,
1529:82
1524:,
1504:,
1489:68
1487:,
1468:22
1461:,
1439:,
1391:,
1369:,
1354:44
1349:,
1334:44
1298:,
1279:.
704:.
479:).
2183:)
1907:)
1903:/
1899:(
1809:)
1791:e
1784:t
1777:v
1764:.
1762:.
1744:.
1708:)
1705:B
1702:(
1697:p
1693:)
1689:H
1686:L
1683:(
1509:2
1446:3
1422:.
1376:1
1329:,
1305:1
1267:X
1247:)
1238:X
1234:,
1231:X
1228:(
1199:X
1178:X
1124:)
1118:,
1115:X
1112:(
1040:)
1034:,
1031:X
1028:(
965:)
959:,
956:X
953:(
947:)
941:,
938:X
935:(
932::
929:j
883:)
877:,
874:X
871:(
851:X
828:,
805:X
779:X
715:X
692:X
666:X
653:x
625:|
621:)
616:n
612:x
608:(
599:x
594:|
583:1
580:=
577:n
550:n
546:x
532:1
529:=
526:n
491:X
467:X
423:X
416:A
412::
368:A
344:)
335:X
331:,
328:X
325:(
302:X
282:X
260:n
256:x
242:1
239:=
236:n
203:k
199:n
194:x
180:1
177:=
174:k
149:X
123:n
119:x
105:1
102:=
99:n
68:X
43:X
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