880:
769:
432:
595:
722:
577:
553:
445:
534:
425:
341:
804:
449:
600:
656:
883:
605:
590:
418:
620:
865:
625:
819:
743:
860:
676:
610:
914:
909:
904:
712:
513:
585:
809:
840:
784:
748:
227:
345:
823:
789:
727:
441:
231:
173:) be the Banach algebra of bounded operators on a Hilbert space. The set of invertible elements in
814:
681:
68:
794:
401:
393:
361:
311:
64:
799:
717:
686:
666:
651:
646:
641:
478:
661:
615:
563:
558:
529:
410:
100:
85:
28:
488:
850:
702:
503:
381:
322:
296:
212:
154:
108:
32:
898:
855:
779:
508:
493:
483:
17:
845:
498:
468:
774:
764:
671:
473:
707:
547:
543:
539:
329:
384:. In other words, for Fredholm operators, the two notions of index coincide.
215:
is a Banach algebra, with the topology of uniform convergence. A function in
246:
224:
405:
149:, being the component of an open set, is both open and closed in
414:
276:
as representatives in G of distinct homotopy classes of maps
199:
denote the unit circle in the complex plane. The algebra
833:
757:
736:
695:
634:
576:
522:
457:
770:Spectral theory of ordinary differential equations
376:is isomorphic to the additive group of integers
370:is again a countable discrete group. In fact, Λ
295:is the set of homotopy classes, indexed by the
426:
8:
461:
433:
419:
411:
35:can be associated with a group called its
723:Group algebra of a locally compact group
223:) is invertible (meaning that it has a
7:
398:An Introduction to Operator Algebras
344:. Suppose π is the quotient map. By
318:. It is a countable discrete group.
234:) if it does not map any element of
55:the group of invertible elements in
25:
181:) is path connected. Therefore, Λ
31:, a branch of mathematics, every
879:
878:
805:Topological quantum field theory
261:. One can choose the functions
207:) of continuous functions from
1:
601:Uniform boundedness principle
400:, CRC Press, Boca Raton, LA,
88:containing the identity 1 of
348:, an invertible elements in
931:
744:Invariant subspace problem
874:
464:
713:Spectrum of a C*-algebra
284:. Thus the index group Λ
257:, the constant function
51:be a Banach algebra and
810:Noncommutative geometry
153:, the index group is a
866:Tomita–Takesaki theory
841:Approximation property
785:Calculus of variations
340:) with respect to the
299:of its members. Thus Λ
228:multiplicative inverse
192:is the trivial group.
84:or in other words the
861:Banach–Mazur distance
824:Generalized functions
310:is isomorphic to the
253:, to the identity in
245:consists of elements
606:Kakutani fixed-point
591:Riesz representation
230:, not that it is an
136:abstract index group
37:abstract index group
18:Abstract index group
790:Functional calculus
749:Mahler's conjecture
728:Von Neumann algebra
442:Functional analysis
364:. The index group Λ
238:to zero. The group
232:invertible function
86:connected component
815:Riemann hypothesis
514:Topological vector
362:Fredholm operators
346:Atkinson's theorem
69:identity component
892:
891:
795:Integral operator
572:
571:
352:is of the form π(
342:compact operators
312:fundamental group
65:topological group
16:(Redirected from
922:
882:
881:
800:Jones polynomial
718:Operator algebra
462:
435:
428:
421:
412:
328:is the quotient
21:
930:
929:
925:
924:
923:
921:
920:
919:
915:Discrete groups
910:Banach algebras
905:Operator theory
895:
894:
893:
888:
870:
834:Advanced topics
829:
753:
732:
691:
657:Hilbert–Schmidt
630:
621:Gelfand–Naimark
568:
518:
453:
439:
390:
375:
369:
309:
294:
266:
244:
213:complex numbers
191:
163:
148:
130:
119:
101:normal subgroup
98:
79:
67:. Consider the
45:
29:operator theory
23:
22:
15:
12:
11:
5:
928:
926:
918:
917:
912:
907:
897:
896:
890:
889:
887:
886:
875:
872:
871:
869:
868:
863:
858:
853:
851:Choquet theory
848:
843:
837:
835:
831:
830:
828:
827:
817:
812:
807:
802:
797:
792:
787:
782:
777:
772:
767:
761:
759:
755:
754:
752:
751:
746:
740:
738:
734:
733:
731:
730:
725:
720:
715:
710:
705:
703:Banach algebra
699:
697:
693:
692:
690:
689:
684:
679:
674:
669:
664:
659:
654:
649:
644:
638:
636:
632:
631:
629:
628:
626:Banach–Alaoglu
623:
618:
613:
608:
603:
598:
593:
588:
582:
580:
574:
573:
570:
569:
567:
566:
561:
556:
554:Locally convex
551:
537:
532:
526:
524:
520:
519:
517:
516:
511:
506:
501:
496:
491:
486:
481:
476:
471:
465:
459:
455:
454:
440:
438:
437:
430:
423:
415:
409:
408:
389:
386:
382:Fredholm index
371:
365:
323:Calkin algebra
300:
297:winding number
285:
264:
242:
182:
162:
159:
155:discrete group
146:
132:
131:
128:
115:
109:quotient group
96:
82:
81:
77:
63:is open and a
44:
41:
33:Banach algebra
24:
14:
13:
10:
9:
6:
4:
3:
2:
927:
916:
913:
911:
908:
906:
903:
902:
900:
885:
877:
876:
873:
867:
864:
862:
859:
857:
856:Weak topology
854:
852:
849:
847:
844:
842:
839:
838:
836:
832:
825:
821:
818:
816:
813:
811:
808:
806:
803:
801:
798:
796:
793:
791:
788:
786:
783:
781:
780:Index theorem
778:
776:
773:
771:
768:
766:
763:
762:
760:
756:
750:
747:
745:
742:
741:
739:
737:Open problems
735:
729:
726:
724:
721:
719:
716:
714:
711:
709:
706:
704:
701:
700:
698:
694:
688:
685:
683:
680:
678:
675:
673:
670:
668:
665:
663:
660:
658:
655:
653:
650:
648:
645:
643:
640:
639:
637:
633:
627:
624:
622:
619:
617:
614:
612:
609:
607:
604:
602:
599:
597:
594:
592:
589:
587:
584:
583:
581:
579:
575:
565:
562:
560:
557:
555:
552:
549:
545:
541:
538:
536:
533:
531:
528:
527:
525:
521:
515:
512:
510:
507:
505:
502:
500:
497:
495:
492:
490:
487:
485:
482:
480:
477:
475:
472:
470:
467:
466:
463:
460:
456:
451:
447:
443:
436:
431:
429:
424:
422:
417:
416:
413:
407:
403:
399:
395:
392:
391:
387:
385:
383:
379:
374:
368:
363:
359:
355:
351:
347:
343:
339:
335:
331:
327:
324:
319:
317:
313:
307:
303:
298:
292:
288:
283:
279:
275:
271:
267:
260:
256:
252:
248:
241:
237:
233:
229:
226:
222:
218:
214:
210:
206:
202:
198:
193:
189:
185:
180:
176:
172:
168:
160:
158:
156:
152:
145:
141:
137:
127:
123:
118:
113:
112:
111:
110:
106:
102:
95:
91:
87:
76:
73:
72:
71:
70:
66:
62:
58:
54:
50:
42:
40:
38:
34:
30:
19:
846:Balanced set
820:Distribution
758:Applications
611:Krein–Milman
596:Closed graph
397:
377:
372:
366:
357:
353:
349:
337:
333:
325:
320:
315:
305:
301:
290:
286:
281:
277:
273:
269:
262:
258:
254:
250:
239:
235:
220:
216:
208:
204:
200:
196:
194:
187:
183:
178:
174:
170:
166:
164:
150:
143:
139:
135:
133:
125:
121:
116:
104:
93:
89:
83:
74:
60:
56:
52:
48:
46:
36:
26:
775:Heat kernel
765:Hardy space
672:Trace class
586:Hahn–Banach
548:Topological
899:Categories
708:C*-algebra
523:Properties
388:References
380:, via the
330:C*-algebra
142:. Because
59:. The set
43:Definition
682:Unbounded
677:Transpose
635:Operators
564:Separable
559:Reflexive
544:Algebraic
530:Barrelled
394:Zhu, Kehe
247:homotopic
225:pointwise
884:Category
696:Algebras
578:Theorems
535:Complete
504:Schwartz
450:glossary
406:27680761
396:(1993).
356:) where
161:Examples
687:Unitary
667:Nuclear
652:Compact
647:Bounded
642:Adjoint
616:Min–max
509:Sobolev
494:Nuclear
484:Hilbert
479:Fréchet
444: (
211:to the
134:is the
662:Normal
499:Orlicz
489:Hölder
469:Banach
458:Spaces
446:topics
404:
107:. The
474:Besov
360:is a
249:, in
99:is a
822:(or
540:Dual
402:OCLC
321:The
272:) =
195:Let
165:Let
47:Let
332:of
314:of
138:of
103:of
27:In
901::
448:–
157:.
120:=
92:;
39:.
826:)
550:)
546:/
542:(
452:)
434:e
427:t
420:v
378:Z
373:K
367:K
358:T
354:T
350:K
338:H
336:(
334:L
326:K
316:T
308:)
306:T
304:(
302:C
293:)
291:T
289:(
287:C
282:T
280:→
278:T
274:z
270:z
268:(
265:n
263:f
259:1
255:G
251:G
243:0
240:G
236:T
221:T
219:(
217:C
209:T
205:T
203:(
201:C
197:T
190:)
188:H
186:(
184:L
179:H
177:(
175:L
171:H
169:(
167:L
151:G
147:0
144:G
140:A
129:0
126:G
124:/
122:G
117:A
114:Λ
105:G
97:0
94:G
90:A
80:,
78:0
75:G
61:G
57:A
53:G
49:A
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.