Operator spaces:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
2000
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society monographs
New series ; 23 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 363 S. |
| ISBN: | 0198534825 |
Staff View
MARC
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| 100 | 1 | |a Effros, Edward G. |e Verfasser |0 (DE-588)1011427591 |4 aut | |
| 245 | 1 | 0 | |a Operator spaces |c Edward G. Effros ; Zhong-Jin Ruan |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford |b Clarendon Press |c 2000 | |
| 300 | |a XVI, 363 S. | ||
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Record in the Search Index
| _version_ | 1804128673533526016 |
|---|---|
| adam_text | Contents
1 Matrix and operator conventions 1
1.1 Matrices and matrix coefficients 1
1.2 Schatten matrix norms 7
1.3 Matrices of operators 10
I Examples and Three Basic Theorems
2 The representation theorem 19
2.1 Concrete and abstract operator spaces 19
2.2 Completely bounded linear mappings 23
2.3 The representation theorem 28
2.4 Notes and references 35
3 Constructions and examples 37
3.1 Subspaces, quotients, products, and conjugates 37
3.2 Dual spaces and mapping spaces 40
3.3 The min and max quantizations 47
3.4 Column and row Hilbert operator spaces 54
3.5 Pisier s self dual Hilbert operator spaces 60
3.6 Notes and references 63
4 The extension theorem 65
4.1 The Arveson Wittstock theorem and injectivity 65
4.2 Duality for subspaces and quotients 74
4.3 Notes and references 76
5 Operator systems and decompositions 77
5.1 Operator systems and complete positivity 77
5.2 The Stinespring theorem and its consequences 83
5.3 Decompositions of complete contractions 86
5.4 Decomposability 93
5.5 Matrix convexity and the trace class operators 101
5.6 Notes and references 103
xiv Contents
6 Injectivity 105
6.1 The injective operator spaces 105
6.2 Injective envelopes 113
6.3 Notes and references 116
II Tensor Products
7 The projective tensor product 123
7.1 Definition and elementary properties 123
7.2 Trace class operators and a Fubini theorem 132
7.3 Notes and references 136
8 The injective tensor product 137
8.1 Definition and elementary properties 137
8.2 Relating Banach and operator space tensor prod¬
ucts 145
8.3 Notes and references 147
0 The Haagerup tensor product 148
9.1 Multiplicatively bounded mappings 149
9.2 The tensor product and its elementary properties 152
9.3 Some tensor product computations 160
9.4 Multilinear decompositions 163
9.5 Notes and references 173
10 Infinite matrices and asymptotic constructions 175
10.1 Infinite matrices over an operator space 175
10.2 Representing elements of the projective tensor prod¬
uct 183
10.3 Ultraproducts 184
10.4 Notes and references 191
III The Grothendieck Programme
11 The approximation property 195
11.1 The Grothendieck approximation property 196
11.2 The operator space approximation property 197
11.3 Tomiyama s slice mapping property 203
11.4 Notes and references 206
Contents xv
12 Mapping spaces 207
12.1 Nuclear and integral mappings of Banach spaces 207
12.2 Completely nuclear mappings 210
12.3 Completely integral mappings 216
12.4 Notes and references 223
13 Absolutely summing mappings 224
13.1 1 summing mappings of Banach spaces 224
13.2 Completely 1 summing mappings 229
13.3 Hilbert space factorable mappings 234
13.4 The Dvoretzky Rogers theorem for operator spaces 238
13.5 Notes and references 239
IV Local Theory and Integrality
14 Local reflexivity, exactness, and nuclearity 243
14.1 The local structure of Banach spaces 243
14.2 The Archbold Batty conditions 247
14.3 Local reflexivity and condition C 252
14.4 Exactness and condition C 260
14.5 Examples of non exact operator spaces 270
14.6 Nuclear operator spaces 276
14.7 Notes and references 282
15 Local reflexivity and exact integrality 284
15.1 The Junge approximation theorem 284
15.2 Exactly integral mappings I 285
15.3 Strong local reflexivity for von Neumann algebra
preduals 287
15.4 Exactly integral mappings II 291
15.5 Relating the mapping spaces 299
15.6 Notes and references 303
V Some Algebraic Applications
16 Non commutative harmonic analysis 307
16.1 Quantized Banach algebras 307
16.2 Operator amenability for Fourier algebras 316
16.3 Notes and references 321
xvi Contents
17 An abstract characterization for non self adjoint
operator algebras 322
17.1 Quantized function algebras 322
17.2 Notes and references 327
Appendix: Preliminaries 330
A.I Linear spaces 330
A.2 Banach spaces 331
A.3 Hilbert spaces 336
A.4 C* algebras and von Neumann algebras 337
A.5 A brief list of operator algebras 341
A.6 Asymptotic products and ultraproducts of Banach
spaces 343
References 347
Index of Notation 355
Index 359
|
| any_adam_object | 1 |
| author | Effros, Edward G. Ruan, Zhong-Jin 1955- |
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| id | DE-604.BV013840152 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:52:59Z |
| institution | BVB |
| isbn | 0198534825 |
| language | English |
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| physical | XVI, 363 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Clarendon Press |
| record_format | marc |
| series | London Mathematical Society monographs |
| series2 | London Mathematical Society monographs : New series |
| spelling | Effros, Edward G. Verfasser (DE-588)1011427591 aut Operator spaces Edward G. Effros ; Zhong-Jin Ruan 1. publ. Oxford Clarendon Press 2000 XVI, 363 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society monographs : New series 23 Banach, Espaces de Banach, Espaces de ram Banachruimten gtt Théorie quantique Théorie quantique ram Quantentheorie Banach spaces Quantum theory Operatorraum (DE-588)4591231-2 gnd rswk-swf Operatorraum (DE-588)4591231-2 s DE-604 Ruan, Zhong-Jin 1955- Verfasser (DE-588)1011427982 aut London Mathematical Society monographs New series ; 23 (DE-604)BV045355493 23 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009466935&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Effros, Edward G. Ruan, Zhong-Jin 1955- Operator spaces London Mathematical Society monographs Banach, Espaces de Banach, Espaces de ram Banachruimten gtt Théorie quantique Théorie quantique ram Quantentheorie Banach spaces Quantum theory Operatorraum (DE-588)4591231-2 gnd |
| subject_GND | (DE-588)4591231-2 |
| title | Operator spaces |
| title_auth | Operator spaces |
| title_exact_search | Operator spaces |
| title_full | Operator spaces Edward G. Effros ; Zhong-Jin Ruan |
| title_fullStr | Operator spaces Edward G. Effros ; Zhong-Jin Ruan |
| title_full_unstemmed | Operator spaces Edward G. Effros ; Zhong-Jin Ruan |
| title_short | Operator spaces |
| title_sort | operator spaces |
| topic | Banach, Espaces de Banach, Espaces de ram Banachruimten gtt Théorie quantique Théorie quantique ram Quantentheorie Banach spaces Quantum theory Operatorraum (DE-588)4591231-2 gnd |
| topic_facet | Banach, Espaces de Banachruimten Théorie quantique Quantentheorie Banach spaces Quantum theory Operatorraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009466935&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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