C*-algebras and finite-dimensional approximations:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2008
|
| Series: | Graduate studies in mathematics
88 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 509 S. graph. Darst. 26 cm |
| ISBN: | 9780821843819 0821843818 |
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MARC
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| 245 | 1 | 0 | |a C*-algebras and finite-dimensional approximations |c Nathaniel P. Brown ; Narutaka Ozawa |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2008 | |
| 300 | |a XV, 509 S. |b graph. Darst. |c 26 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 88 | |
| 650 | 4 | |a C*-algèbres | |
| 650 | 4 | |a Groupes finis | |
| 650 | 4 | |a C*-algebras | |
| 650 | 4 | |a Finite groups | |
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| 830 | 0 | |a Graduate studies in mathematics |v 88 |w (DE-604)BV009739289 |9 88 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016522409 | ||
Record in the Search Index
| _version_ | 1804137690416807936 |
|---|---|
| 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
|
| adam_txt |
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 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Brown, Nathanial P. 1972- Ozawa, Narutaka 1974- |
| author_GND | (DE-588)140461159 (DE-588)140461108 |
| author_facet | Brown, Nathanial P. 1972- Ozawa, Narutaka 1974- |
| author_role | aut aut |
| author_sort | Brown, Nathanial P. 1972- |
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| callnumber-search | QA326 |
| callnumber-sort | QA 3326 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)180190949 (DE-599)BVBBV023338590 |
| dewey-full | 512/.556 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.556 |
| dewey-search | 512/.556 |
| dewey-sort | 3512 3556 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV023338590 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:00:44Z |
| indexdate | 2024-07-09T21:16:18Z |
| institution | BVB |
| isbn | 9780821843819 0821843818 |
| language | English |
| lccn | 2007060566 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016522409 |
| oclc_num | 180190949 |
| open_access_boolean | |
| 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 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Brown, Nathanial P. 1972- Verfasser (DE-588)140461159 aut C*-algebras and finite-dimensional approximations Nathaniel P. Brown ; Narutaka Ozawa Providence, RI American Math. Soc. 2008 XV, 509 S. graph. Darst. 26 cm txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 88 C*-algèbres Groupes finis C*-algebras Finite groups Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf C-Stern-Algebra (DE-588)4136693-1 gnd rswk-swf C-Stern-Algebra (DE-588)4136693-1 s Endliche Gruppe (DE-588)4014651-0 s DE-604 Ozawa, Narutaka 1974- Verfasser (DE-588)140461108 aut Erscheint auch als Online-Ausgabe 978-1-4704-2118-2 Graduate studies in mathematics 88 (DE-604)BV009739289 88 Digitalisierung UB Regensburg application/pdf 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 Inhaltsverzeichnis |
| 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_exact_search_txtP | 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 |