Theory of Operator Spaces by Edward G Effros

Theory of Operator Spaces by Edward G Effros

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.

Edward G. Effros, University of Illinois at Urbana-Champaign, IL.

Zhong-Jin Ruan, University of Illinois at Urbana-Champaign, IL.

SKU	Unavailable
ISBN 13	9781470465056
ISBN 10	1470465051
Title	Theory of Operator Spaces
Author	Edward G Effros
Series	Ams Chelsea Publishing
Condition	Unavailable
Binding Type	Paperback
Publisher	American Mathematical Society
Year published	2022-07-30
Number of pages	358
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.