Holdings: An introduction to the classification of amenable C*-Algebras

An introduction to the classification of amenable C*-Algebras:

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Bibliographic Details
Main Author:	Lin, Huaxin (Author)
Format:	Book
Language:	English
Published:	Singapore [u.a.] World Scientific 2001
Subjects:	Análise funcional C* álgebras C-algebra's C-algèbres K-théorie C*-algebras K-theory Klassifikation C-Stern-Algebra
Online Access:	Inhaltsverzeichnis
Item Description:	Includes bibliographical references (p. 307-316) and index
Physical Description:	XI, 320 S.
ISBN:	9810246803

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MARC


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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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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
work_keys_str_mv	AT linhuaxin anintroductiontotheclassificationofamenablecalgebras

Holdings

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