Tensor Products Of C Algebras And Operator Spaces
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Tensor Products of C*-algebras and Operator Spaces
Author: Gilles Pisier
language: en
Publisher: Cambridge University Press
Release Date: 2020-02-27
Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.
C*-Algebras and Operator Theory
This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.
Introduction to Operator Space Theory
Author: Gilles Pisier
language: en
Publisher: Cambridge University Press
Release Date: 2003-08-25
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.