Theory of Operator Spaces (Paperback)

Edward G. Effros

ISBN 10: 1470465051 / ISBN 13: 9781470465056

Published by American Mathematical Society, Providence, 2022

About this Item

Paperback. This book provides the main results and ideas in the theories of completely bounded maps, operator spaces, and operator algebras, along with some of their main applications. It requires only a basic background in functional analysis to read through the book. The descriptions and discussions of the topics are self-explained. It is appropriate for graduate students new to the subject and the field.The book starts with the basic representation theorems for abstract operator spaces and their mappings, followed by a discussion of tensor products and the analogue of Grothendieck's approximation property. Next, the operator space analogues of the nuclear, integral, and absolutely summing mappings are discussed. In what is perhaps the deepest part of the book, the authors present the remarkable ""non-classical"" phenomena that occur when one considers local reflexivity and exactness for operator spaces. This is an area of great beauty and depth, and it represents one of the triumphs of the subject. In the final part of the book, the authors consider applications to non-commutative harmonic analysis and non-self-adjoint operator algebra theory.Operator space theory provides a synthesis of Banach space theory with the non-commuting variables of operator algebra theory, and it has led to exciting new approaches in both disciplines. This book is an indispensable introduction to the theory of operator spaces. Provides the main results and ideas in the theories of completely bounded maps, operator spaces, and operator algebras, along with some of their main applications. The descriptions and discussions of the topics are self-explained. The book is appropriate for graduate students new to the subject and the field. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9781470465056

Bibliographic Details

• Title: Theory of Operator Spaces (Paperback)
• Publisher: American Mathematical Society, Providence
• Publication Date: 2022
• Language: English
• ISBN 10: 1470465051
• ISBN 13: 9781470465056
• Binding: Paperback
• Condition: new

About this title

Synopsis

This book provides the main results and ideas in the theories of completely bounded maps, operator spaces, and operator algebras, along with some of their main applications. It requires only a basic background in functional analysis to read through the book. The descriptions and discussions of the topics are self-explained. It is appropriate for graduate students new to the subject and the field. The book starts with the basic representation theorems for abstract operator spaces and their mappings, followed by a discussion of tensor products and the analogue of Grothendieck's approximation property. Next, the operator space analogues of the nuclear, integral, and absolutely summing mappings are discussed. In what is perhaps the deepest part of the book, the authors present the remarkable “non-classical” phenomena that occur when one considers local reflexivity and exactness for operator spaces. This is an area of great beauty and depth, and it represents one of the triumphs of the subject. In the final part of the book, the authors consider applications to non-commutative harmonic analysis and non-self-adjoint operator algebra theory. Operator space theory provides a synthesis of Banach space theory with the non-commuting variables of operator algebra theory, and it has led to exciting new approaches in both disciplines. This book is an indispensable introduction to the theory of operator spaces.

About the Author

Edward G. Effros, and Zhong-Jin Ruan, University of Illinois at Urbana-Champaign, IL