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Tensor Products of C*-Algebras and Operator Spaces: The Connes-Kirchberg Problem

Paperback / softback

Main Details

Title Tensor Products of C*-Algebras and Operator Spaces: The Connes-Kirchberg Problem
Authors and Contributors      By (author) Gilles Pisier
SeriesLondon Mathematical Society Student Texts
Physical Properties
Format:Paperback / softback
Pages:494
Dimensions(mm): Height 227,Width 153
Category/GenreAlgebra
Calculus and mathematical analysis
Probability and statistics
ISBN/Barcode 9781108749114
ClassificationsDewey:512.556
Audience
Professional & Vocational
Illustrations Worked examples or Exercises

Publishing Details

Publisher Cambridge University Press
Imprint Cambridge University Press
Publication Date 27 February 2020
Publication Country United Kingdom

Description

Based on the author's university lecture courses, this book presents the many facets of one of the most important open problems in operator algebra theory. Central to this book is the proof of the equivalence of the various forms of the problem, including forms involving C*-algebra tensor products and free groups, ultraproducts of von Neumann algebras, and quantum information theory. The reader is guided through a number of results (some of them previously unpublished) revolving around tensor products of C*-algebras and operator spaces, which are reminiscent of Grothendieck's famous Banach space theory work. The detailed style of the book and the inclusion of background information make it easily accessible for beginning researchers, Ph.D. students, and non-specialists alike.

Author Biography

Gilles Pisier is Emeritus Professor at Sorbonne Universite and Distinguished Professor at Texas A & M University. He is the author of several books, including Introduction to Operator Space Theory (Cambridge, 2003) and Martingales in Banach Spaces (Cambridge, 2016). His multiple awards include the Salem prize in 1979 and the Ostrowski Prize in 1997, and he was the plenary speaker at the International Congress of Mathematicians in 1998.

Reviews

'This is a very rich and detailed monograph on an enormously important subject. It is written in the crystal clear and elegant style that is the hallmark of its author, and it offers a lot of information to specialists and novices alike. The book will certainly become an authoritative guide.' Dirk Werner, London Mathematical Society Student Texts 'This book is jam packed with information, and should be an invaluable guide to anyone interested in these ideas ... For the complete picture and the recent advances, Pisier's book is the place to go.' Bulletin of the American Mathematical Society