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C*-algebras and finite-dimensional approximations:

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Main Authors:	Brown, Nathanial P. 1972- (Author), Ozawa, Narutaka 1974- (Author)
Format:	Book
Language:	English
Published:	Providence, RI American Math. Soc. 2008
Series:	Graduate studies in mathematics 88
Subjects:	C-algèbres Groupes finis C-algebras Finite groups Endliche Gruppe C-Stern-Algebra
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016522409&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XV, 509 S. graph. Darst. 26 cm
ISBN:	9780821843819 0821843818

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Record in the Search Index

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adam_text	Contents Preface Xl Chapter 1. Fundamental Facts 1 §1.1. Notation 1 §1.2. C-algebras 2 §1.3. Von Neumann algebras 3 §1.4. Double duals 5 §1.5. Completely positive maps 9 §1.6. Arveson s Extension Theorem 17 §1.7. Voiculescu s Theorem 18 Part 1. Basic Theory Chapter 2. Nuclear and Exact C-Algebras: Definitions, Basic Facts and Examples 25 §2.1. Nuclear maps 25 §2.2. Nonunital technicalities 28 §2.3. Nuclear and exact C-algebras 32 §2.4. First examples 38 §2.5. C-algebras associated to discrete groups 42 §2.6. Amenable groups 48 §2.7. Type I C-algebras 55 §2.8. References 58 Chapter 3. Tensor Products 59 vi Contents §3.1. Algebraic tensor products 59 §3.2. Analytic preliminaries 66 §3.3. The spatial and maximal C -norms 72 §3.4. Takesaki s Theorem 77 §3.5. Continuity of tensor product maps 82 §3.6. Inclusions and The Trick 85 §3.7. Exact sequences 92 §3.8. Nuclearity and tensor products 99 §3.9. Exactness and tensor products 105 §3.10. References 112 Chapter 4. Constructions 115 §4.1. Crossed products 115 §4.2. Integer actions 121 §4.3. Amenable actions 124 §4.4. X x Г -algebras 129 §4.5. Compact group actions and graph C-algebras 133 §4.6. Cuntz-Pimsner algebras 136 §4.7. Reduced amalgamated free products 154 §4.8. Maps on reduced amalgamated free products 157 §4.9. References 165 Chapter 5. Exact Groups and Related Topics 167 §5.1. Exact groups 167 §5.2. Groups acting on trees 176 §5.3. Hyperbolic groups 182 §5.4. Subgroups of Lie groups 193 §5.5. Coarse metric spaces 194 §5.6. Groupoids 200 §5.7. References 209 Chapter 6. Amenable Traces and Kirchberg s Factorization Property 211 §6.1. Traces and the right regular representation 211 §6.2. Amenable traces 214 §6.3. Some motivation and examples 223 §6.4. The factorization property and Kazhdan s property (T) 227 §6.5. References 235 Contents Vil Chapter 7. Quasidiagonal C-Algebras 237 §7.1. The definition, easy examples and obstructions 237 §7.2. The representation theorem 243 §7.3. Homotopy invariance 247 §7.4. Two more examples 252 §7.5. External approximation 255 §7.6. References 260 Chapter 8. AF Embeddability 261 §8.1. Stable uniqueness and asymptotically commuting diagrams 261 §8.2. Cones over exact RFD algebras 267 §8.3. Cones over general exact algebras 268 §8.4. Homotopy invariance 274 §8.5. A survey 279 §8.6. References 282 Chapter 9. Local Reflexivity and Other Tensor Product Conditions 283 §9.1. Local reflexivity 284 §9.2. Tensor product properties 285 §9.3. Equivalence of exactness and property С 293 §9.4. Corollaries 297 §9.5. References 299 Chapter 10. Summary and Open Problems 301 §10.1. Nuclear C-algebras 301 §10.2. Exact C-algebras 303 §10.3. Quasidiagonal C*-algebras 306 §10.4. Open problems 309 Part 2. Special Topics Chapter 11. Simple ^-Algebras 313 §11.1. Generalized inductive limits 313 §11.2. NF and strong NF algebras 317 §11.3. Inner quasidiagonality 323 §11.4. Excision and Popa s technique 328 §11.5. Connes s uniqueness theorem 335 §11.6. References 337 viii Contents Chapter 12. Approximation Properties for Groups 339 §12.1. Kazhdan s property (T) 339 §12.2. The Haagerup property 354 §12.3. Weak amenability 361 §12.4. Another approximation property 369 §12.5. References 374 Chapter 13. Weak Expectation Property and Local Lifting Property 375 §13.1. The local lifting property 375 §13.2. Tensorial characterizations of the LLP and WEP 378 §13.3. The QWEP conjecture 380 §13.4. Nonsemisplit extensions 385 §13.5. Norms on B^2) Θ B^2) 388 §13.6. References 391 Chapter 14. Weakly Exact von Neumann Algebras 393 §14.1. Definition and examples 393 §14.2. Characterization of weak exactness 397 §14.3. References 403 Part 3. Applications Chapter 15. Classification of Group von Neumann Algebras 407 §15.1. Subalgebras with noninjective relative commutants 407 §15.2. On bi-exactness 411 §15.3. Examples 414 §15.4. References 420 Chapter 16. Herrero s Approximation Problem 421 §16.1. Description of the problem 421 §16.2. ^-preliminaries 423 §16.3. Resolution of Herrero s problem 425 §16.4. Counterexamples 426 §16.5. References 429 Chapter 17. Counterexamples in K-Homology and K-Theory 431 §17.1. BDF preliminaries 431 §17.2. Property (T) and Kazhdan projections 435 §17.3. Ext need not be a group 438 Contents ix §17.4. Topology on Ext 439 §17.5. References 441 Part 4. Appendices Appendix A. Ultrafilters and Ultraproducts 445 Appendix B. Operator Spaces, Completely Bounded Maps and Duality 449 Appendix С Lifting Theorems 459 Appendix D. Positive Definite Functions, Cocycles and Schoenberg s Theorem 463 Appendix E. Groups and Graphs 471 Appendix F. Bimodules over von Neumann Algebras 479 Bibliography 493 Notation Index 5°3 Subject Index 505
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id	DE-604.BV023338590
illustrated	Illustrated
indexdate	2024-12-20T13:13:56Z
institution	BVB
isbn	9780821843819 0821843818
language	English
lccn	2007060566
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016522409
oclc_num	180190949
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owner	DE-824 DE-355 DE-BY-UBR DE-83 DE-11 DE-188
owner_facet	DE-824 DE-355 DE-BY-UBR DE-83 DE-11 DE-188
physical	XV, 509 S. graph. Darst. 26 cm
publishDate	2008
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publishDateSort	2008
publisher	American Math. Soc.
record_format	marc
series	Graduate studies in mathematics
series2	Graduate studies in mathematics
spellingShingle	Brown, Nathanial P. 1972- Ozawa, Narutaka 1974- C-algebras and finite-dimensional approximations Graduate studies in mathematics C-algèbres Groupes finis C*-algebras Finite groups Endliche Gruppe (DE-588)4014651-0 gnd C-Stern-Algebra (DE-588)4136693-1 gnd
subject_GND	(DE-588)4014651-0 (DE-588)4136693-1
title	C*-algebras and finite-dimensional approximations
title_auth	C*-algebras and finite-dimensional approximations
title_exact_search	C*-algebras and finite-dimensional approximations
title_full	C*-algebras and finite-dimensional approximations Nathaniel P. Brown ; Narutaka Ozawa
title_fullStr	C*-algebras and finite-dimensional approximations Nathaniel P. Brown ; Narutaka Ozawa
title_full_unstemmed	C*-algebras and finite-dimensional approximations Nathaniel P. Brown ; Narutaka Ozawa
title_short	C*-algebras and finite-dimensional approximations
title_sort	c algebras and finite dimensional approximations
topic	C-algèbres Groupes finis C-algebras Finite groups Endliche Gruppe (DE-588)4014651-0 gnd C-Stern-Algebra (DE-588)4136693-1 gnd
topic_facet	C-algèbres Groupes finis C-algebras Finite groups Endliche Gruppe C-Stern-Algebra
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016522409&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV009739289
work_keys_str_mv	AT brownnathanialp calgebrasandfinitedimensionalapproximations AT ozawanarutaka calgebrasandfinitedimensionalapproximations

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