Crossed products of C*-algebras:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2007]
|
| Series: | Mathematical surveys and monographs
Volume 134 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | xvi, 528 Seiten |
| ISBN: | 0821842420 9780821842423 |
Staff View
MARC
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| 245 | 1 | 0 | |a Crossed products of C*-algebras |c Dana P. Williams |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2007] | |
| 264 | 4 | |c © 2007 | |
| 300 | |a xvi, 528 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v Volume 134 | |
| 650 | 7 | |a Análise funcional |2 larpcal | |
| 650 | 7 | |a C* álgebras |2 larpcal | |
| 650 | 7 | |a Álgebras de operadores |2 larpcal | |
| 650 | 4 | |a C*-algebras | |
| 650 | 4 | |a Operator algebras | |
| 650 | 0 | 7 | |a C-Stern-Algebra |0 (DE-588)4136693-1 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
| 689 | 0 | |5 DE-604 | |
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| 830 | 0 | |a Mathematical surveys and monographs |v Volume 134 |w (DE-604)BV000018014 |9 134 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016420028 | ||
Record in the Search Index
| _version_ | 1804137528645648384 |
|---|---|
| adam_text | Contents
Introduction
xi
1
Locally Compact Groups
1
1.1
Preliminaries on Topological Groups
.................. 2
1.2
Preliminaries on Locally Compact Groups
............... 5
1.3 Haar
Measure
............................... 16
1.4
An Interlude: Abelian Harmonic Analysis
............... 22
1.5
Integration on Groups
.......................... 28
2
Dynamical Systems and Crossed Products
41
2.1
Dynamical Systems
............................ 41
2.2
Covariant Representations
........................ 44
2.3
The Crossed Product
........................... 47
2.4
Representations of the Crossed Product
................ 54
2.5
Comments on Examples
......................... 64
2.6
Universal Property
............................ 72
3
Special Cases and Basic Constructions
81
3.1
Another Interlude: The C*-Algebra of an Abelian group
....... 81
3.2
Third Interlude: The C-Algebra of a Compact group
........ 84
3.3
Semidirect Products
........................... 86
3.4
Invariant Ideals
.............................. 92
3.5
The Orbit Space
............................. 94
3.6
Proper Actions and Induced Algebras
................. 99
4
Imprimitivity Theorems
109
4.1
The Symmetric Imprimitivity Theorem
................ 110
4.2
Some Special Cases
............................ 125
4.3
Green s Imprimitivity Theorem
..................... 130
4.4
The Stone-von Neumann Theorem
................... 133
4.5
Transitive Transformation Groups
................... 137
vii
viii Contents
5
Induced Representations and Induced Ideals
151
5.1
Induced Representations of Crossed Products
.............151
5.2
An Example
................................161
5.3
Inducing Ideals
..............................164
5.4
Invariant Ideals and the Induction Process
...............166
6
Orbits and Quasi-orbits
171
6.1
The Mackey-Glimm Dichotomy
.....................171
6.2
The Res Map and Quasi-Orbits
.....................179
7
Properties of Crossed Products
189
7.1
The Takai Duality Theorem
.......................189
7.2
The Reduced Crossed Product
.....................197
7.3
Crossed Products Involving the Compacts
...............203
7.4
Aside on Twisted Crossed Products
..................208
7.5
The Type Structure of Regular Crossed Products
...........221
8
Ideal Structure
227
8.1
Fibering Over the Orbit Space
.....................227
8.2
EH-Regularity and the GRS-Theorem
.................239
8.3
The Ideal Structure of Co(X) xlt
G
...................242
8.4
The Fell Subgroup Crossed Product
..................256
9
The Proof of the GRS-Theorem
261
9.1
Step I: Induced Primitive Ideals
.....................268
9.2
Step II: Restricting to the Stability Groups
..............271
9.3
Step III: Sauvageot s Induced Representation
.............283
9.4
Step IV:
G
Amenable
..........................292
9.5
Step V: Gootman-Rosenberg a la Renault
...............298
Appendices
A Amenable Groups
311
A.I States and Positive Definite Functions
.................311
A.2 Amenability
................................318
A.3 Another GNS Construction
.......................327
В
The Banach
*-
Algebra £1(G, A)
331
B.I Vector-Valued Integration
........................331
B.2 Product Measures
............................344
С
Bundles of C*-algebras
353
C.I CoW-algebras
..............................354
C.2 Upper Semicontinuous C*-bundles
...................360
Contents ix
D
Groups
369
D.I Group homomorphisms
.........................369
D.2
Borei
Groups and Invariant Measures
.................374
D.3
Projective
Representations
........................379
D.4 Quasi-invariant Measures
........................387
D.5 Technical Results
.............................391
E
Representations of C*-algebras
399
E.I Multiplicity
................................399
E.2 Decomposable Operators
.........................405
F
Direct Integrals
409
F.I
Borei
Hubert Bundles
.......................... 409
F.2 The Direct Integral of Hubert Spaces
.................. 413
F.3 Decomposable Operators
......................... 416
F.4
т
-isomorphisms..............................
421
F.5 Uniqueness of Direct Integrals
...................... 422
F.6 Isomorphism Bundle
........................... 427
F.7 Product
Borei
Structure
......................... 427
F.8 Measurable Sections
........................... 429
G Effros s
Ideal Center Decomposition
431
G.I Effros s Ideal Center Decomposition
..................431
G.2 Ideal Center Decompositions of Covariant Representations
......445
H
The Fell Topology
453
H.I The Fell Topology
............................453
H.2 Basic Results
...............................456
H.3 Bruhat Approximate Cross Sections
..................465
H.4 The Stabilizer Map
............................469
H.5
Borei
Issues
................................473
H.6 PrimA Standard
.............................474
I Miscellany
479
1.1 The Internal Tensor Product
...................... 479
1.2
Disintegration of Measures
........................ 481
1.3
Abelian
Von
Neumann Algebras
.................... 488
1.4
The Hubert Space L2(G.H)
....................... 490
1.5
The Dual of Ll{G)
............................ 495
1.6
Point Maps
................................ 498
1.7
Representations of
C0{X)
........................ 503
1.8
Invariants of Morita Equivalent C*-Algebras
.............. 507
Notation and Symbol Index
509
Index
513
Bibliography
521
|
| adam_txt |
Contents
Introduction
xi
1
Locally Compact Groups
1
1.1
Preliminaries on Topological Groups
. 2
1.2
Preliminaries on Locally Compact Groups
. 5
1.3 Haar
Measure
. 16
1.4
An Interlude: Abelian Harmonic Analysis
. 22
1.5
Integration on Groups
. 28
2
Dynamical Systems and Crossed Products
41
2.1
Dynamical Systems
. 41
2.2
Covariant Representations
. 44
2.3
The Crossed Product
. 47
2.4
Representations of the Crossed Product
. 54
2.5
Comments on Examples
. 64
2.6
Universal Property
. 72
3
Special Cases and Basic Constructions
81
3.1
Another Interlude: The C*-Algebra of an Abelian group
. 81
3.2
Third Interlude: The C-Algebra of a Compact group
. 84
3.3
Semidirect Products
. 86
3.4
Invariant Ideals
. 92
3.5
The Orbit Space
. 94
3.6
Proper Actions and Induced Algebras
. 99
4
Imprimitivity Theorems
109
4.1
The Symmetric Imprimitivity Theorem
. 110
4.2
Some Special Cases
. 125
4.3
Green's Imprimitivity Theorem
. 130
4.4
The Stone-von Neumann Theorem
. 133
4.5
Transitive Transformation Groups
. 137
vii
viii Contents
5
Induced Representations and Induced Ideals
151
5.1
Induced Representations of Crossed Products
.151
5.2
An Example
.161
5.3
Inducing Ideals
.164
5.4
Invariant Ideals and the Induction Process
.166
6
Orbits and Quasi-orbits
171
6.1
The Mackey-Glimm Dichotomy
.171
6.2
The Res Map and Quasi-Orbits
.179
7
Properties of Crossed Products
189
7.1
The Takai Duality Theorem
.189
7.2
The Reduced Crossed Product
.197
7.3
Crossed Products Involving the Compacts
.203
7.4
Aside on Twisted Crossed Products
.208
7.5
The Type Structure of Regular Crossed Products
.221
8
Ideal Structure
227
8.1
Fibering Over the Orbit Space
.227
8.2
EH-Regularity and the GRS-Theorem
.239
8.3
The Ideal Structure of Co(X) xlt
G
.242
8.4
The Fell Subgroup Crossed Product
.256
9
The Proof of the GRS-Theorem
261
9.1
Step I: Induced Primitive Ideals
.268
9.2
Step II: Restricting to the Stability Groups
.271
9.3
Step III: Sauvageot's Induced Representation
.283
9.4
Step IV:
G
Amenable
.292
9.5
Step V: Gootman-Rosenberg a la Renault
.298
Appendices
A Amenable Groups
311
A.I States and Positive Definite Functions
.311
A.2 Amenability
.318
A.3 Another GNS Construction
.327
В
The Banach
*-
Algebra £1(G, A)
331
B.I Vector-Valued Integration
.331
B.2 Product Measures
.344
С
Bundles of C*-algebras
353
C.I CoW-algebras
.354
C.2 Upper Semicontinuous C*-bundles
.360
Contents ix
D
Groups
369
D.I Group homomorphisms
.369
D.2
Borei
Groups and Invariant Measures
.374
D.3
Projective
Representations
.379
D.4 Quasi-invariant Measures
.387
D.5 Technical Results
.391
E
Representations of C*-algebras
399
E.I Multiplicity
.399
E.2 Decomposable Operators
.405
F
Direct Integrals
409
F.I
Borei
Hubert Bundles
. 409
F.2 The Direct Integral of Hubert Spaces
. 413
F.3 Decomposable Operators
. 416
F.4
т
-isomorphisms.
421
F.5 Uniqueness of Direct Integrals
. 422
F.6 Isomorphism Bundle
. 427
F.7 Product
Borei
Structure
. 427
F.8 Measurable Sections
. 429
G Effros's
Ideal Center Decomposition
431
G.I Effros's Ideal Center Decomposition
.431
G.2 Ideal Center Decompositions of Covariant Representations
.445
H
The Fell Topology
453
H.I The Fell Topology
.453
H.2 Basic Results
.456
H.3 Bruhat Approximate Cross Sections
.465
H.4 The Stabilizer Map
.469
H.5
Borei
Issues
.473
H.6 PrimA Standard
.474
I Miscellany
479
1.1 The Internal Tensor Product
. 479
1.2
Disintegration of Measures
. 481
1.3
Abelian
Von
Neumann Algebras
. 488
1.4
The Hubert Space L2(G.H)
. 490
1.5
The Dual of Ll{G)
. 495
1.6
Point Maps
. 498
1.7
Representations of
C0{X)
. 503
1.8
Invariants of Morita Equivalent C*-Algebras
. 507
Notation and Symbol Index
509
Index
513
Bibliography
521 |
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| id | DE-604.BV023234388 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T20:21:23Z |
| indexdate | 2024-07-09T21:13:44Z |
| institution | BVB |
| isbn | 0821842420 9780821842423 |
| language | English |
| lccn | 2006047931 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016420028 |
| oclc_num | 76794891 |
| open_access_boolean | 1 |
| owner | DE-355 DE-BY-UBR DE-11 DE-19 DE-BY-UBM |
| owner_facet | DE-355 DE-BY-UBR DE-11 DE-19 DE-BY-UBM |
| physical | xvi, 528 Seiten |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Williams, Dana P. 1952- Verfasser (DE-588)137464924 aut Crossed products of C*-algebras Dana P. Williams Providence, Rhode Island American Mathematical Society [2007] © 2007 xvi, 528 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 134 Análise funcional larpcal C* álgebras larpcal Álgebras de operadores larpcal C*-algebras Operator algebras C-Stern-Algebra (DE-588)4136693-1 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf C-Stern-Algebra (DE-588)4136693-1 s Dynamisches System (DE-588)4013396-5 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1361-3 Mathematical surveys and monographs Volume 134 (DE-604)BV000018014 134 http://www.gbv.de/dms/goettingen/52170975X.pdf kostenfrei Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016420028&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Williams, Dana P. 1952- Crossed products of C*-algebras Mathematical surveys and monographs Análise funcional larpcal C* álgebras larpcal Álgebras de operadores larpcal C*-algebras Operator algebras C-Stern-Algebra (DE-588)4136693-1 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4136693-1 (DE-588)4013396-5 |
| title | Crossed products of C*-algebras |
| title_auth | Crossed products of C*-algebras |
| title_exact_search | Crossed products of C*-algebras |
| title_exact_search_txtP | Crossed products of C*-algebras |
| title_full | Crossed products of C*-algebras Dana P. Williams |
| title_fullStr | Crossed products of C*-algebras Dana P. Williams |
| title_full_unstemmed | Crossed products of C*-algebras Dana P. Williams |
| title_short | Crossed products of C*-algebras |
| title_sort | crossed products of c algebras |
| topic | Análise funcional larpcal C* álgebras larpcal Álgebras de operadores larpcal C*-algebras Operator algebras C-Stern-Algebra (DE-588)4136693-1 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Análise funcional C* álgebras Álgebras de operadores C*-algebras Operator algebras C-Stern-Algebra Dynamisches System |
| url | http://www.gbv.de/dms/goettingen/52170975X.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016420028&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT williamsdanap crossedproductsofcalgebras |
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