Similarity Problems and Completely Bounded Maps (Lecture Notes in Mathematics)

Gilles Pisier

ISBN 10: 3540603220 / ISBN 13: 9783540603221

Published by Springer, 1995

About this Item

Cover has some light shelfwear. Pages are clean and intact. There is some slight dirtiness on the textblock/fore edge from handling.

Seller Inventory # mon0002858817

Bibliographic Details

• Title: Similarity Problems and Completely Bounded Maps (Lecture Notes in Mathematics)
• Publisher: Springer
• Publication Date: 1995
• Language: English
• ISBN 10: 3540603220
• ISBN 13: 9783540603221
• Binding: Paperback
• Condition: Very Good

About this title

Synopsis

This book is mainly about three similarity problems arising in three different contexts, namely group representations, C*-algebras and uniform algebras (e.g. the disc algebra). These three problems (all still open in full generality) are studied using a common tool, completely bounded maps, which have recently emerged as a major concept in operator algebra theory. The book is devoted to the background necessary to understand these problems, to the partial solutions that are known and to numerous related concepts and results. The book is mostly self-contained and accessible to graduate students mastering basic functional and harmonic analysis. For advanced readers, it can be an invitation to the recently developed theory of "operator spaces", for which completely bounded maps are the fundamental morphisms.

From the Back Cover

These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* -algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. While the three problems seem different, it is possible to place them in a common framework using the key concept of "complete boundedness", which we present in detail. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying certain additional algebraic identities. Two chapters have been added on the HALMOS and KADISON similarity problems.