Introduction to operator space theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2003
|
| Series: | London Mathematical Society lecture note series
294 |
| Subjects: | |
| Online Access: | Table of contents Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | VII, 478 S. |
| ISBN: | 0521811651 |
Staff View
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| 245 | 1 | 0 | |a Introduction to operator space theory |c Gilles Pisier |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
0. Introduction 1
Part I. INTRODUCTION TO OPERATOR SPACES
1. Completely bounded maps 17
2. The minimal tensor product. Ruan s theorem. Basic operations 28
2.1. Minimal tensor product 28
2.2. Ruan s theorem 34
2.3. Dual space 40
2.4. Quotient space 42
Quotient by a subspace 42
Quotient by an ideal 43
2.5. Bidual. Von Neumann algebras 47
2.6. Direct sum 51
2.7. Intersection, sum, complex interpolation 52
2.8. Ultraproduct 59
2.9. Complex conjugate 63
2.10. Opposite 64
2.11. Ruan s theorem and quantization 65
2.12. Universal objects 67
2.13. Perturbation lemmas 68
3. Minimal and maximal operator space structures 71
4. Projective tensor product 81
5. The Haagerup tensor product 86
Basic properties 86
Multilinear factorization 92
Injectivity/projectivity 93
Self duality 93
Free products 98
Factorization through R or C 101
Symmetrized Haagerup tensor product 102
Complex interpolation 106
6. Characterizations of operator algebras 109
7. The operator Hilbert space 122
Hilbertian operator spaces 122
Existence and unicity of OH. Basic properties 122
Finite dimensional estimates 130
Complex interpolation 135
Vector valued Lp spaces, either commutative
or noncommutative 138
8. Group C* algebras. Universal algebras and unitization
for an operator space 148
9. Examples and comments 165
9.1. A concrete quotient: Hankel matrices 165
vi Contents
9.2. Homogeneous operator spaces 172
9.3. Fermions. Antisymmetric Fock space. Spin systems 173
9.4. The Cuntz algebra On 175
9.5. The operator space structure of the classical Lp spaces 178
9.6. The C* algebra of the free group with n generators 182
9.7. Reduced C* algebra of the free group with
n generators 183
9.8. Operator space generated in the usual Lp space
by Gaussain random variables or by the
Rademacher functions 191
9.9. Semi circular systems in Voiculescu s sense 200
9.10. Embeddings of von Neumann algebras into ultraproducts 210
9.11. Dvoretzky s theorem 215
10. Comparisons 217
Part II. OPERATOR SPACES AND C* TENSOR PRODUCTS
11. C* norms on tensor products. Decomposable maps. Nuclearity 227
12. Nuclearity and approximation properties 240
13. C*{¥X)®B{H) 252
14. Kirchberg s theorem on decomposable maps 261
15. The Weak Expectation Property (WEP) 267
16. The Local Lifting Property (LLP) 275
17. Exactness 285
18. Local reflexivity 303
Basic properties 303
A conjecture on local reflexivity and OLLP 305
Properties C,C and C . Exactness versus local reflexivity 309
19. Grothendieck s theorem for operator spaces 316
20. Estimating the norms of sums of unitaries: Ramanujan
graphs, property T, random matrices 324
21. Local theory of operator spaces. Nonseparability of OSn 334
22. B{H) ® B{H) 348
23. Completely isomorphic C* algebras 354
24. Injective and projective operator spaces 356
Part III. OPERATOR SPACES AND NON SELF ADJOINT
OPERATOR ALGEBRAS
25. Maximal tensor products and free products of
operator algebras 365
26. The Blecher Paulsen factorization. Infinite Haagerup
tensor products 384
27. Similarity problems 396
28. The Sz. Nagy Halmos similarity problem 407
Solutions to the exercises 418
Contents vii
References 457
Subject index 477
Notation index 479
|
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| indexdate | 2024-07-09T19:05:26Z |
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| isbn | 0521811651 |
| language | English |
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| physical | VII, 478 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
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| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spelling | Pisier, Gilles 1950- Verfasser (DE-588)113782268 aut Introduction to operator space theory Gilles Pisier Cambridge [u.a.] Cambridge Univ. Press 2003 VII, 478 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 294 Includes bibliographical references and index Espaces d'opérateurs Operator spaces Operatorraum (DE-588)4591231-2 gnd rswk-swf Operatorraum (DE-588)4591231-2 s DE-604 London Mathematical Society lecture note series 294 (DE-604)BV000000130 294 http://www.loc.gov/catdir/toc/cam031/2002031358.html Table of contents http://www.loc.gov/catdir/description/cam0210/2002031358.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009976536&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pisier, Gilles 1950- Introduction to operator space theory London Mathematical Society lecture note series Espaces d'opérateurs Operator spaces Operatorraum (DE-588)4591231-2 gnd |
| subject_GND | (DE-588)4591231-2 |
| title | Introduction to operator space theory |
| title_auth | Introduction to operator space theory |
| title_exact_search | Introduction to operator space theory |
| title_full | Introduction to operator space theory Gilles Pisier |
| title_fullStr | Introduction to operator space theory Gilles Pisier |
| title_full_unstemmed | Introduction to operator space theory Gilles Pisier |
| title_short | Introduction to operator space theory |
| title_sort | introduction to operator space theory |
| topic | Espaces d'opérateurs Operator spaces Operatorraum (DE-588)4591231-2 gnd |
| topic_facet | Espaces d'opérateurs Operator spaces Operatorraum |
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