An introduction to the classification of amenable C*-Algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2001
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 307-316) and index |
| Beschreibung: | XI, 320 S. |
| ISBN: | 9810246803 |
Internformat
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| 650 | 7 | |a C*-algebra's |2 gtt | |
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Datensatz im Suchindex
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| adam_text | AN INTRODUCTION TO THE CLASSIFICATION OF AMENABLE C-ALGEBRAS HUAXIN LIN
UNIVERSITY OF OREGON, USA WORLD SCIENTIFIC NEW JERSEY *LONDON *
SINGAPORE * HONG KONG * BANGALORE CONTENTS PREFACE VII CHAPTER 1 THE
BASICS OF C*-ALGEBRAS 1 1.1 BANACH ALGEBRAS 1 1.2 C*-ALGEBRAS 9 1.3
COMMUTATIVE C*-ALGEBRAS 12 1.4 POSITIVE CONES 16 1.5 APPROXIMATE
IDENTITIES, HEREDITARY C*-SUBALGEBRAS AND QUOTIENTS 20 1.6 POSITIVE
LINEAR FUNCTIONALS AND A GELFAND-NAIMARK THEOREM . . 25 1.7 VON NEUMANN
ALGEBRAS 32 1.8 ENVELOPING VON NEUMANN ALGEBRAS AND THE SPECTRAL THEOREM
38 1.9 EXAMPLES OF C*-ALGEBRAS 42 1.10 INDUCTIVE LIMITS OF C*-ALGEBRAS
51 1.11 EXERCISES 60 1.12 ADDENDA 65 CHAPTER 2 AMENABLE C*-ALGEBRAS AND
IF-THEORY 67 2.1 COMPLETELY POSITIVE LINEAR MAPS AND THE STINESPRING
REPRESEN- TATION 67 2.2 EXAMPLES OF COMPLETELY POSITIVE LINEAR MAPS 72
2.3 AMENABLE C*-ALGEBRAS 76 2.4 K-THEORY 82 2.5 PERTURBATIONS 89 2.6
EXAMPLES OF IF-GROUPS . . : 97 IX X CONTENTS 2.7 IF-THEORY OF INDUCTIVE
LIMITS OF C*-ALGEBRAS 103 2.8 EXERCISES 108 2.9 ADDENDA ILL CHAPTER 3
AF-ALGEBRAS AND RANKS OF C*-ALGEBRAS 113 3.1 C*-ALGEBRAS OF STABLE RANK
ONE AND THEIR .RT-THEORY 113 3.2 C*-ALGEBRAS OF LOWER RANK 120 3.3 ORDER
STRUCTURE OF IF-THEORY 127 3.4 AF-ALGEBRAS 133 3.5 SIMPLE C*-ALGEBRAS
140 3.6 TRACIAL TOPOLOGICAL RANK 146 3.7 SIMPLE C*-ALGEBRAS WITH TR(A)
1 154 3.8 EXERCISES 160 3.9 ADDENDA 162 CHAPTER 4 CLASSIFICATION OF
SIMPLE AT-ALGEBRAS 165 4.1 SOME BASICS ABOUT ^4T-ALGEBRAS 165 4.2
UNITARY GROUPS OF C*-ALGEBRAS WITH REAL RANK ZERO 170 4.3 SIMPLE
AT-ALGEBRAS WITH REAL RANK ZERO 177 4.4 UNITARIES IN SIMPLE C*-ALGEBRA
WITH RR(A) =0 182 4.5 A UNIQUENESS THEOREM 186 4.6 CLASSIFICATION OF
SIMPLE .AT-ALGEBRAS 192 -4.7 INVARIANTS OF SIMPLE AT-ALGEBRAS 196 4.8
EXERCISES 204 4.9 ADDENDA 208 CHAPTER 5 C*-ALGEBRA EXTENSIONS 211 5.1
MULTIPLIER ALGEBRAS 211 5.2 EXTENSIONS OF C*-ALGEBRAS 217 5.3 COMPLETELY
POSITIVE MAPS TO M N (C) 221 5.4 AMENABLE COMPLETELY POSITIVE MAPS 227
5.5 ABSORBING EXTENSIONS 233 5.6 A STABLE UNIQUENESS THEOREM 243 5.7
/T-THEORY AND THE UNIVERSAL COEFFICIENT THEOREM 250 5.8 CHARACTERIZATION
OF KK-THEORY AND A UNIVERSAL MULTI-COEFFICIENT THEOREM 255 5.9
APPROXIMATELY TRIVIAL EXTENSIONS 259 5.10 EXERCISES 265 CONTENTS XI
CHAPTER 6 CLASSIFICATION OF SIMPLE AMENABLE C*-ALGEBRAS 269 6.1 AN
EXISTENCE THEOREM 269 6.2 SIMPLE AH-ALGEBRAS 279 6.3 THE CLASSIFICATION
THEOREMS 288 6.4 INVARIANTS AND SOME ISOMORPHISM THEOREMS 295
BIBLIOGRAPHY 307 INDEX 317
|
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512.55 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV014229577 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:59:59Z |
| institution | BVB |
| isbn | 9810246803 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009754965 |
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| physical | XI, 320 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Lin, Huaxin Verfasser aut An introduction to the classification of amenable C*-Algebras Huaxin Lin Singapore [u.a.] World Scientific 2001 XI, 320 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 307-316) and index Análise funcional larpcal C* álgebras larpcal C*-algebra's gtt C*-algèbres K-théorie C*-algebras K-theory Klassifikation (DE-588)4030958-7 gnd rswk-swf C-Stern-Algebra (DE-588)4136693-1 gnd rswk-swf C-Stern-Algebra (DE-588)4136693-1 s Klassifikation (DE-588)4030958-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009754965&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lin, Huaxin An introduction to the classification of amenable C*-Algebras Análise funcional larpcal C* álgebras larpcal C*-algebra's gtt C*-algèbres K-théorie C*-algebras K-theory Klassifikation (DE-588)4030958-7 gnd C-Stern-Algebra (DE-588)4136693-1 gnd |
| subject_GND | (DE-588)4030958-7 (DE-588)4136693-1 |
| title | An introduction to the classification of amenable C*-Algebras |
| title_auth | An introduction to the classification of amenable C*-Algebras |
| title_exact_search | An introduction to the classification of amenable C*-Algebras |
| title_full | An introduction to the classification of amenable C*-Algebras Huaxin Lin |
| title_fullStr | An introduction to the classification of amenable C*-Algebras Huaxin Lin |
| title_full_unstemmed | An introduction to the classification of amenable C*-Algebras Huaxin Lin |
| title_short | An introduction to the classification of amenable C*-Algebras |
| title_sort | an introduction to the classification of amenable c algebras |
| topic | Análise funcional larpcal C* álgebras larpcal C*-algebra's gtt C*-algèbres K-théorie C*-algebras K-theory Klassifikation (DE-588)4030958-7 gnd C-Stern-Algebra (DE-588)4136693-1 gnd |
| topic_facet | Análise funcional C* álgebras C*-algebra's C*-algèbres K-théorie C*-algebras K-theory Klassifikation C-Stern-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009754965&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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