22:
462:
514:
738:
582:
400:
762:
538:
370:
346:
322:
268:
244:
220:
166:
142:
668:
625:
298:
196:
101:
of representations of C*-algebras. It implies that, for irreducible representations of C*-algebras, the only non-zero linear invariant subspace is the whole space.
708:
688:
558:
866:
405:
79:
875:
796:
112:
there is no reason to believe that all topologically irreducible representations are also algebraically irreducible.
65:
43:
36:
467:
890:
98:
719:
563:
381:
743:
519:
351:
327:
303:
249:
225:
201:
147:
123:
30:
630:
587:
47:
818:
277:
175:
97:
that, in effect, asserts the equivalence of the notions of topological irreducibility and
8:
822:
693:
673:
543:
841:
871:
846:
792:
836:
826:
861:
806:
784:
105:
857:
780:
884:
850:
831:
94:
86:
457:{\displaystyle {\mathcal {H}},\{y_{1},\cdots ,y_{n}\}}
746:
722:
696:
676:
633:
590:
566:
546:
522:
470:
408:
384:
354:
330:
306:
280:
252:
228:
204:
178:
150:
126:
740:
acts topologically irreducibly on the
Hilbert space
402:
acts topologically irreducibly on the
Hilbert space
756:
732:
702:
682:
662:
619:
576:
552:
532:
508:
456:
394:
364:
340:
316:
292:
262:
238:
214:
190:
160:
136:
882:
867:Fundamentals of the Theory of Operator Algebras
789:Fundamentals of the Theory of Operator Algebras
516:is a linearly independent set of vectors in
503:
471:
451:
419:
287:
281:
185:
179:
222:are the only closed stable subspaces under
764:, then it acts algebraically irreducibly.
840:
830:
809:(1957), "Irreducible operator algebras",
66:Learn how and when to remove this message
144:of bounded operators on a Hilbert space
29:This article includes a list of general
805:
509:{\displaystyle \{x_{1},\cdots ,x_{n}\}}
883:
15:
870:, Vol. I : Elementary Theory,
791:, Vol. I : Elementary Theory,
725:
569:
387:
13:
749:
710:can be chosen to be self-adjoint.
525:
411:
357:
333:
309:
255:
231:
207:
153:
129:
35:it lacks sufficient corresponding
14:
902:
324:are the only linear manifolds in
20:
733:{\displaystyle {\mathfrak {A}}}
670:for some self-adjoint operator
577:{\displaystyle {\mathfrak {A}}}
395:{\displaystyle {\mathfrak {A}}}
773:
757:{\displaystyle {\mathcal {H}}}
533:{\displaystyle {\mathcal {H}}}
365:{\displaystyle {\mathcal {F}}}
341:{\displaystyle {\mathcal {H}}}
317:{\displaystyle {\mathcal {H}}}
263:{\displaystyle {\mathcal {F}}}
239:{\displaystyle {\mathcal {F}}}
215:{\displaystyle {\mathcal {H}}}
161:{\displaystyle {\mathcal {H}}}
137:{\displaystyle {\mathcal {F}}}
80:Kadison's theorem generalizing
1:
811:Proc. Natl. Acad. Sci. U.S.A.
767:
93:is a result in the theory of
663:{\displaystyle Bx_{j}=y_{j}}
620:{\displaystyle Ax_{j}=y_{j}}
115:
91:Kadison transitivity theorem
7:
10:
907:
77:
272:algebraically irreducibly
170:topologically irreducibly
464:is a set of vectors and
99:algebraic irreducibility
78:Not to be confused with
104:The theorem, proved by
50:more precise citations.
758:
734:
704:
684:
664:
621:
578:
554:
534:
510:
458:
396:
366:
342:
318:
294:
264:
240:
216:
192:
162:
138:
832:10.1073/pnas.43.3.273
759:
735:
705:
685:
665:
622:
579:
555:
535:
511:
459:
397:
378:. If the C*-algebra
367:
343:
319:
295:
293:{\displaystyle \{0\}}
265:
241:
217:
193:
191:{\displaystyle \{0\}}
163:
139:
744:
720:
716:. If the C*-algebra
694:
674:
631:
588:
564:
544:
520:
468:
406:
382:
352:
328:
304:
278:
250:
226:
202:
176:
148:
124:
108:, was surprising as
823:1957PNAS...43..273K
754:
730:
700:
680:
660:
617:
574:
550:
530:
506:
454:
392:
362:
338:
314:
290:
260:
236:
212:
188:
158:
134:
891:Operator algebras
703:{\displaystyle A}
683:{\displaystyle B}
553:{\displaystyle A}
82:Wigner's theorem.
76:
75:
68:
898:
853:
844:
834:
807:Kadison, Richard
799:
777:
763:
761:
760:
755:
753:
752:
739:
737:
736:
731:
729:
728:
709:
707:
706:
701:
689:
687:
686:
681:
669:
667:
666:
661:
659:
658:
646:
645:
626:
624:
623:
618:
616:
615:
603:
602:
583:
581:
580:
575:
573:
572:
559:
557:
556:
551:
539:
537:
536:
531:
529:
528:
515:
513:
512:
507:
502:
501:
483:
482:
463:
461:
460:
455:
450:
449:
431:
430:
415:
414:
401:
399:
398:
393:
391:
390:
371:
369:
368:
363:
361:
360:
347:
345:
344:
339:
337:
336:
323:
321:
320:
315:
313:
312:
299:
297:
296:
291:
269:
267:
266:
261:
259:
258:
245:
243:
242:
237:
235:
234:
221:
219:
218:
213:
211:
210:
197:
195:
194:
189:
167:
165:
164:
159:
157:
156:
143:
141:
140:
135:
133:
132:
71:
64:
60:
57:
51:
46:this article by
37:inline citations
24:
23:
16:
906:
905:
901:
900:
899:
897:
896:
895:
881:
880:
862:Ringrose, J. R.
802:
785:Ringrose, J. R.
779:Theorem 5.4.3;
778:
774:
770:
748:
747:
745:
742:
741:
724:
723:
721:
718:
717:
695:
692:
691:
675:
672:
671:
654:
650:
641:
637:
632:
629:
628:
611:
607:
598:
594:
589:
586:
585:
568:
567:
565:
562:
561:
545:
542:
541:
524:
523:
521:
518:
517:
497:
493:
478:
474:
469:
466:
465:
445:
441:
426:
422:
410:
409:
407:
404:
403:
386:
385:
383:
380:
379:
356:
355:
353:
350:
349:
332:
331:
329:
326:
325:
308:
307:
305:
302:
301:
279:
276:
275:
270:is said to act
254:
253:
251:
248:
247:
230:
229:
227:
224:
223:
206:
205:
203:
200:
199:
177:
174:
173:
168:is said to act
152:
151:
149:
146:
145:
128:
127:
125:
122:
121:
118:
106:Richard Kadison
83:
72:
61:
55:
52:
42:Please help to
41:
25:
21:
12:
11:
5:
904:
894:
893:
879:
878:
876:978-0821808191
858:Kadison, R. V.
855:
817:(3): 273–276,
801:
800:
797:978-0821808191
781:Kadison, R. V.
771:
769:
766:
751:
727:
699:
679:
657:
653:
649:
644:
640:
636:
614:
610:
606:
601:
597:
593:
571:
549:
540:, there is an
527:
505:
500:
496:
492:
489:
486:
481:
477:
473:
453:
448:
444:
440:
437:
434:
429:
425:
421:
418:
413:
389:
359:
335:
311:
289:
286:
283:
257:
233:
209:
187:
184:
181:
155:
131:
117:
114:
74:
73:
28:
26:
19:
9:
6:
4:
3:
2:
903:
892:
889:
888:
886:
877:
873:
869:
868:
863:
859:
856:
852:
848:
843:
838:
833:
828:
824:
820:
816:
812:
808:
804:
803:
798:
794:
790:
786:
782:
776:
772:
765:
715:
711:
697:
677:
655:
651:
647:
642:
638:
634:
612:
608:
604:
599:
595:
591:
547:
498:
494:
490:
487:
484:
479:
475:
446:
442:
438:
435:
432:
427:
423:
416:
377:
373:
348:stable under
284:
273:
246:. The family
182:
171:
113:
111:
107:
102:
100:
96:
92:
88:
81:
70:
67:
59:
56:November 2014
49:
45:
39:
38:
32:
27:
18:
17:
865:
814:
810:
788:
775:
713:
712:
375:
374:
271:
169:
119:
109:
103:
90:
84:
62:
53:
34:
95:C*-algebras
87:mathematics
48:introducing
768:References
584:such that
31:references
714:Corollary
488:⋯
436:⋯
120:A family
116:Statement
885:Category
851:16590013
110:a priori
819:Bibcode
690:, then
376:Theorem
44:improve
874:
849:
842:528430
839:
795:
33:, but
627:. If
172:when
872:ISBN
847:PMID
793:ISBN
300:and
198:and
837:PMC
827:doi
560:in
274:if
85:In
887::
864:,
860:;
845:,
835:,
825:,
815:43
813:,
787:,
783:;
372:.
89:,
854:.
829::
821::
750:H
726:A
698:A
678:B
656:j
652:y
648:=
643:j
639:x
635:B
613:j
609:y
605:=
600:j
596:x
592:A
570:A
548:A
526:H
504:}
499:n
495:x
491:,
485:,
480:1
476:x
472:{
452:}
447:n
443:y
439:,
433:,
428:1
424:y
420:{
417:,
412:H
388:A
358:F
334:H
310:H
288:}
285:0
282:{
256:F
232:F
208:H
186:}
183:0
180:{
154:H
130:F
69:)
63:(
58:)
54:(
40:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.