Introduction to Operator Space Theory by Gilles Pisier 0000-00-00 00:00:00

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by Gilles Pisier
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Introduction to Operator Space Theory by Gilles Pisier
Author
Gilles Pisier
Publisher
Cambridge University Press
Date of release
Pages
488
ISBN
9780521811651
Binding
Paperback
Illustrations
Format
PDF, EPUB, MOBI, TXT, DOC
Rating
5
48
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Book review

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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