Introduction to operator space theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, U.K.
Cambridge University Press
2003
|
| Schriftenreihe: | London Mathematical Society lecture note series
294 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. [457]-475) and indexes Introduction to Operator Spaces -- Completely bounded maps -- Minimal tensor product -- Minimal and maximal operator space structures on a Banach space -- Projective tensor product -- The Haagerup tensor product -- Characterizations of operator algebras -- The operator Hilbert space -- Group C*-algebras -- Examples and comments -- Comparisons -- Operator Spaces and C*-tensor products -- C*-norms on tensor products -- Nuclearity and approximation properties -- C* -- Kirchberg's theorem on decomposable maps -- The weak expectation property -- The local lifting property -- Exactness -- Local reflexivity -- Grothendieck's theorem for operator spaces -- Estimating the norms of sums of unitaries -- Local theory of operator spaces -- Completely isomorphic C*-algebras -- Injective and projective operator spaces -- Operator Spaces and Non Self-Adjoint Operator Algebras -- Maximal tensor products and free products of non self-adjoint operator algebras -- The Blechter-Paulsen factorization -- Similarity problems -- The Sz-nagy-halmos similarity problem -- Solutions to the exercises The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. An 'operator space' is simply a Banach space with an embedding into the space B(H) of all bounded operators on a Hilbert space H. The first part of this book is an introduction with emphasis on examples that illustrate various aspects of the theory. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C* algebras. The third (and shorter) part of the book describes applications to non self-adjoint operator algebras, and similarity problems. In particular the author's counterexample to the 'Halmos problem' is presented, as well as work on the new concept of "length" of an operator algebra. Graduate students and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find that this book has much to offer |
| Beschreibung: | 1 Online-Ressource (vii, 478 p.) |
| ISBN: | 0511064519 0511205562 0521811651 1107360234 9780511064517 9780511205569 9780521811651 9781107360235 |
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| 500 | |a Includes bibliographical references (p. [457]-475) and indexes | ||
| 500 | |a Introduction to Operator Spaces -- Completely bounded maps -- Minimal tensor product -- Minimal and maximal operator space structures on a Banach space -- Projective tensor product -- The Haagerup tensor product -- Characterizations of operator algebras -- The operator Hilbert space -- Group C*-algebras -- Examples and comments -- Comparisons -- Operator Spaces and C*-tensor products -- C*-norms on tensor products -- Nuclearity and approximation properties -- C* -- Kirchberg's theorem on decomposable maps -- The weak expectation property -- The local lifting property -- Exactness -- Local reflexivity -- Grothendieck's theorem for operator spaces -- Estimating the norms of sums of unitaries -- Local theory of operator spaces -- Completely isomorphic C*-algebras -- Injective and projective operator spaces -- Operator Spaces and Non Self-Adjoint Operator Algebras -- Maximal tensor products and free products of non self-adjoint operator algebras -- The Blechter-Paulsen factorization -- Similarity problems -- The Sz-nagy-halmos similarity problem -- Solutions to the exercises | ||
| 500 | |a The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. An 'operator space' is simply a Banach space with an embedding into the space B(H) of all bounded operators on a Hilbert space H. The first part of this book is an introduction with emphasis on examples that illustrate various aspects of the theory. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C* algebras. The third (and shorter) part of the book describes applications to non self-adjoint operator algebras, and similarity problems. In particular the author's counterexample to the 'Halmos problem' is presented, as well as work on the new concept of "length" of an operator algebra. Graduate students and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find that this book has much to offer | ||
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Datensatz im Suchindex
| _version_ | 1804175604406288384 |
|---|---|
| any_adam_object | |
| author | Pisier, Gilles |
| author_facet | Pisier, Gilles |
| author_role | aut |
| author_sort | Pisier, Gilles |
| author_variant | g p gp |
| building | Verbundindex |
| bvnumber | BV043148041 |
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| dewey-full | 515/.732 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.732 |
| dewey-search | 515/.732 |
| dewey-sort | 3515 3732 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043148041 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:56Z |
| institution | BVB |
| isbn | 0511064519 0511205562 0521811651 1107360234 9780511064517 9780511205569 9780521811651 9781107360235 |
| language | English |
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| physical | 1 Online-Ressource (vii, 478 p.) |
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| spelling | Pisier, Gilles Verfasser aut Introduction to operator space theory Gilles Pisier Cambridge, U.K. Cambridge University Press 2003 1 Online-Ressource (vii, 478 p.) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 294 Includes bibliographical references (p. [457]-475) and indexes Introduction to Operator Spaces -- Completely bounded maps -- Minimal tensor product -- Minimal and maximal operator space structures on a Banach space -- Projective tensor product -- The Haagerup tensor product -- Characterizations of operator algebras -- The operator Hilbert space -- Group C*-algebras -- Examples and comments -- Comparisons -- Operator Spaces and C*-tensor products -- C*-norms on tensor products -- Nuclearity and approximation properties -- C* -- Kirchberg's theorem on decomposable maps -- The weak expectation property -- The local lifting property -- Exactness -- Local reflexivity -- Grothendieck's theorem for operator spaces -- Estimating the norms of sums of unitaries -- Local theory of operator spaces -- Completely isomorphic C*-algebras -- Injective and projective operator spaces -- Operator Spaces and Non Self-Adjoint Operator Algebras -- Maximal tensor products and free products of non self-adjoint operator algebras -- The Blechter-Paulsen factorization -- Similarity problems -- The Sz-nagy-halmos similarity problem -- Solutions to the exercises The theory of operator spaces is very recent and can be described as a non-commutative Banach space theory. An 'operator space' is simply a Banach space with an embedding into the space B(H) of all bounded operators on a Hilbert space H. The first part of this book is an introduction with emphasis on examples that illustrate various aspects of the theory. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C* algebras. The third (and shorter) part of the book describes applications to non self-adjoint operator algebras, and similarity problems. In particular the author's counterexample to the 'Halmos problem' is presented, as well as work on the new concept of "length" of an operator algebra. Graduate students and professional mathematicians interested in functional analysis, operator algebras and theoretical physics will find that this book has much to offer Espaces d'opérateurs Funktionalanalysis swd Operatorraum swd MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Operator spaces local Operator spaces Operatorraum (DE-588)4591231-2 gnd rswk-swf Operatorraum (DE-588)4591231-2 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=120691 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pisier, Gilles Introduction to operator space theory Espaces d'opérateurs Funktionalanalysis swd Operatorraum swd MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Operator spaces local 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 Funktionalanalysis swd Operatorraum swd MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Operator spaces local Operator spaces Operatorraum (DE-588)4591231-2 gnd |
| topic_facet | Espaces d'opérateurs Funktionalanalysis Operatorraum MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis Operator spaces |
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