Completely Bounded Maps and Operator Algebras

Front Cover
Cambridge University Press, 2002 - Mathematics - 300 pages
0 Reviews
This book tours the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, along with some of their main applications. It requires only a basic background in functional analysis. The presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will appreciate how the author illustrates the power of methods he has developed with new and simpler proofs of some of the major results in the area, many of which have not appeared earlier in the literature. An indispensible introduction to the theory of operator spaces.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Introduction
1
Positive Maps
9
Completely Positive Maps
26
Dilation Theorems
43
Commuting Contractions on Hilbert Space
58
Completely Positive Maps into A
73
Arvesons Extension Theorems
84
Completely Bounded Maps
97
Tensor Products and Joint Spectral Sets
159
Abstract Characterizations of Operator Systems and Operator Spaces
175
An Operator Space Bestiary
186
Injective Envelopes
206
Abstract Operator Algebras
225
Completely Bounded Multilinear Maps and the Haagerup Tensor Norm
239
Universal Operator Algebras and Factorization
260
Similarity and Factorization
273

Completely Bounded Homomorphisms
120
Polynomially Bounded and PowerBounded Operators
135
Applications to ASpectral Sets
150

Common terms and phrases

References to this book

All Book Search results »

Bibliographic information