999:
341:
388:
888:
418:
551:
462:
442:
256:
236:
216:
196:
176:
156:
132:
108:
88:
61:
714:
1028:
841:
696:
672:
564:
653:
544:
510:
264:
923:
568:
135:
719:
489:
485:
64:
775:
1002:
724:
709:
537:
739:
984:
744:
938:
862:
111:
28:
979:
352:
795:
729:
1023:
831:
632:
421:
704:
928:
959:
903:
867:
515:
B Sz.-Nagy and C. Foias, "The "Lifting theorem" for intertwining operators and some new applications",
942:
908:
846:
560:
933:
800:
913:
506:
918:
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805:
785:
770:
765:
760:
597:
396:
780:
734:
682:
677:
648:
529:
524:
Metric
Constrained Interpolation, Commutant Lifting, and Systems. Vol. 100. Springer, 1998
20:
607:
969:
821:
622:
447:
427:
241:
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201:
181:
161:
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117:
93:
73:
46:
1017:
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898:
627:
612:
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68:
32:
964:
617:
587:
893:
883:
790:
592:
826:
666:
662:
658:
465:
472:
can be "lifted" to an operator in the commutant of the unitary dilation of
35:, is a powerful theorem used to prove several interpolation results.
533:
336:{\displaystyle RT^{n}=P_{H}SU^{n}\vert _{H}\;\forall n\geq 0,}
484:
The commutant lifting theorem can be used to prove the left
450:
430:
399:
355:
267:
244:
224:
204:
184:
164:
144:
120:
96:
76:
49:
492:, and the two-sided Nudelman theorem, among others.
952:
876:
855:
814:
753:
695:
641:
576:
889:Spectral theory of ordinary differential equations
456:
436:
412:
382:
335:
250:
230:
210:
190:
170:
150:
126:
102:
82:
55:
545:
503:Completely Bounded Maps and Operator Algebras
43:The commutant lifting theorem states that if
8:
383:{\displaystyle \Vert S\Vert =\Vert R\Vert .}
374:
368:
362:
356:
308:
580:
552:
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530:
317:
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311:
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288:
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243:
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183:
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95:
75:
48:
842:Group algebra of a locally compact group
464:. In other words, an operator from the
7:
318:
14:
998:
997:
924:Topological quantum field theory
134:(which can be shown to exist by
1029:Theorems in functional analysis
1:
720:Uniform boundedness principle
490:Sarason interpolation theorem
486:Nevanlinna-Pick interpolation
114:acting on some Hilbert space
198:, then there is an operator
136:Sz.-Nagy's dilation theorem
1045:
863:Invariant subspace problem
993:
583:
25:commutant lifting theorem
832:Spectrum of a C*-algebra
929:Noncommutative geometry
110:is its minimal unitary
985:Tomita–Takesaki theory
960:Approximation property
904:Calculus of variations
458:
438:
414:
384:
337:
252:
232:
212:
192:
172:
152:
128:
104:
84:
57:
980:Banach–Mazur distance
943:Generalized functions
517:Indiana Univ. Math. J
459:
439:
415:
413:{\displaystyle P_{H}}
385:
338:
253:
233:
213:
193:
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153:
129:
105:
85:
58:
725:Kakutani fixed-point
710:Riesz representation
522:FoiaĹź, Ciprian, ed.
448:
428:
397:
353:
265:
242:
222:
202:
182:
162:
142:
118:
94:
74:
47:
909:Functional calculus
868:Mahler's conjecture
847:Von Neumann algebra
561:Functional analysis
934:Riemann hypothesis
633:Topological vector
519:20 (1971): 901-904
454:
434:
410:
380:
333:
248:
228:
208:
188:
168:
158:is an operator on
148:
124:
100:
80:
53:
1011:
1010:
914:Integral operator
691:
690:
457:{\displaystyle H}
437:{\displaystyle K}
251:{\displaystyle U}
231:{\displaystyle K}
211:{\displaystyle S}
191:{\displaystyle T}
171:{\displaystyle H}
151:{\displaystyle R}
127:{\displaystyle K}
103:{\displaystyle U}
83:{\displaystyle H}
56:{\displaystyle T}
1036:
1001:
1000:
919:Jones polynomial
837:Operator algebra
581:
554:
547:
540:
531:
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109:
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101:
89:
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62:
60:
59:
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16:Operator theorem
1044:
1043:
1039:
1038:
1037:
1035:
1034:
1033:
1024:Operator theory
1014:
1013:
1012:
1007:
989:
953:Advanced topics
948:
872:
851:
810:
776:Hilbert–Schmidt
749:
740:Gelfand–Naimark
687:
637:
572:
558:
498:
482:
446:
445:
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425:
400:
395:
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351:
350:
307:
297:
284:
271:
263:
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238:commuting with
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180:
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178:commuting with
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116:
115:
92:
91:
72:
71:
45:
44:
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21:operator theory
17:
12:
11:
5:
1042:
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1026:
1016:
1015:
1009:
1008:
1006:
1005:
994:
991:
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987:
982:
977:
972:
970:Choquet theory
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962:
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916:
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865:
859:
857:
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844:
839:
834:
829:
824:
822:Banach algebra
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816:
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798:
793:
788:
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778:
773:
768:
763:
757:
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750:
748:
747:
745:Banach–Alaoglu
742:
737:
732:
727:
722:
717:
712:
707:
701:
699:
693:
692:
689:
688:
686:
685:
680:
675:
673:Locally convex
670:
656:
651:
645:
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620:
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610:
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584:
578:
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559:
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556:
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542:
534:
528:
527:
520:
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501:Vern Paulsen,
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407:
403:
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379:
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247:
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187:
167:
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123:
99:
79:
52:
40:
37:
15:
13:
10:
9:
6:
4:
3:
2:
1041:
1030:
1027:
1025:
1022:
1021:
1019:
1004:
996:
995:
992:
986:
983:
981:
978:
976:
975:Weak topology
973:
971:
968:
966:
963:
961:
958:
957:
955:
951:
944:
940:
937:
935:
932:
930:
927:
925:
922:
920:
917:
915:
912:
910:
907:
905:
902:
900:
899:Index theorem
897:
895:
892:
890:
887:
885:
882:
881:
879:
875:
869:
866:
864:
861:
860:
858:
856:Open problems
854:
848:
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843:
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838:
835:
833:
830:
828:
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823:
820:
819:
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802:
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797:
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792:
789:
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767:
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629:
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562:
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543:
541:
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532:
525:
521:
518:
514:
512:
511:0-521-81669-6
508:
504:
500:
499:
495:
493:
491:
488:theorem, the
487:
479:
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467:
451:
431:
423:
405:
401:
377:
371:
365:
359:
349:
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276:
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261:
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259:
245:
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205:
185:
165:
145:
137:
121:
113:
97:
77:
70:
69:Hilbert space
66:
50:
38:
36:
34:
30:
26:
22:
965:Balanced set
939:Distribution
877:Applications
730:Krein–Milman
715:Closed graph
523:
516:
502:
483:
480:Applications
473:
469:
392:
345:
42:
24:
18:
894:Heat kernel
884:Hardy space
791:Trace class
705:Hahn–Banach
667:Topological
65:contraction
1018:Categories
827:C*-algebra
642:Properties
496:References
422:projection
258:such that
801:Unbounded
796:Transpose
754:Operators
683:Separable
678:Reflexive
663:Algebraic
649:Barrelled
466:commutant
375:‖
369:‖
363:‖
357:‖
325:≥
319:∀
39:Statement
27:, due to
1003:Category
815:Algebras
697:Theorems
654:Complete
623:Schwartz
569:glossary
112:dilation
29:Sz.-Nagy
806:Unitary
786:Nuclear
771:Compact
766:Bounded
761:Adjoint
735:Min–max
628:Sobolev
613:Nuclear
603:Hilbert
598:Fréchet
563: (
420:is the
138:), and
781:Normal
618:Orlicz
608:Hölder
588:Banach
577:Spaces
565:topics
509:
505:2002,
393:Here,
23:, the
593:Besov
444:onto
424:from
67:on a
63:is a
33:Foias
941:(or
659:Dual
507:ISBN
346:and
31:and
468:of
218:on
19:In
1020::
567:–
476:.
90:,
945:)
669:)
665:/
661:(
571:)
553:e
546:t
539:v
526:.
474:T
470:T
452:H
432:K
406:H
402:P
378:.
372:R
366:=
360:S
331:,
328:0
322:n
313:H
309:|
303:n
299:U
295:S
290:H
286:P
282:=
277:n
273:T
269:R
246:U
226:K
206:S
186:T
166:H
146:R
122:K
98:U
78:H
51:T
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