Title Introduction to operator space theory / Gilles Pisier

Published Cambridge, U.K. ; New York : Cambridge University Press, 2003

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Description 1 online resource (vii, 478 pages) Series London Mathematical Society lecture note series ; 294 London Mathematical Society lecture note series ; 294. Contents 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 Summary 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 Bibliography Includes bibliographical references (pages 457-475) and indexes Notes Print version record Subject Operator spaces. MATHEMATICS -- Calculus. MATHEMATICS -- Mathematical Analysis. Operator spaces Funktionalanalysis Operatorraum Form Electronic book ISBN 9780511064517 0511064519 9781107360235 1107360234 9780511205569 0511205562 9780511072970 051107297X

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