Softcover ISBN:  9781470465056 
Product Code:  CHEL/386 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 
eBook ISBN:  9781470470357 
Product Code:  CHEL/386.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 
Softcover ISBN:  9781470465056 
eBook: ISBN:  9781470470357 
Product Code:  CHEL/386.B 
List Price:  $120.00 $90.00 
MAA Member Price:  $108.00 $81.00 
AMS Member Price:  $96.00 $72.00 
Softcover ISBN:  9781470465056 
Product Code:  CHEL/386 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 
eBook ISBN:  9781470470357 
Product Code:  CHEL/386.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 
Softcover ISBN:  9781470465056 
eBook ISBN:  9781470470357 
Product Code:  CHEL/386.B 
List Price:  $120.00 $90.00 
MAA Member Price:  $108.00 $81.00 
AMS Member Price:  $96.00 $72.00 

Book DetailsAMS Chelsea PublishingVolume: 386; 2022; 358 ppMSC: Primary 46; Secondary 47
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 selfexplained. 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 “nonclassical” 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 noncommutative harmonic analysis and nonselfadjoint operator algebra theory.
Operator space theory provides a synthesis of Banach space theory with the noncommuting 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.
ReadershipGraduate students and researchers interested in functional analysis and operator theory.

Table of Contents

Chapters

Matrix and operator conventions

Examples and three basic theorems

The representation theorem

Constructions and examples

The extension theorem

Operator systems and decompositions

Injectivity

Tensor products

The projective tensor product

The injective tensor product

The Haagerup tensor product

Infinite matrices and asymptotic constructions

The Grothendieck programme

The approximation property

Mapping spaces

Absolutely summing mappings

Local theory and integrality

Local reflexivity, exactness, and nuclearity

Local reflexivity and exact integrality

Some algebraic applications

Noncommutative harmonic analysis

An abstract characterization for nonselfadjoint operator algebras

Preliminaries


Additional Material

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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 selfexplained. 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 “nonclassical” 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 noncommutative harmonic analysis and nonselfadjoint operator algebra theory.
Operator space theory provides a synthesis of Banach space theory with the noncommuting 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.
Graduate students and researchers interested in functional analysis and operator theory.

Chapters

Matrix and operator conventions

Examples and three basic theorems

The representation theorem

Constructions and examples

The extension theorem

Operator systems and decompositions

Injectivity

Tensor products

The projective tensor product

The injective tensor product

The Haagerup tensor product

Infinite matrices and asymptotic constructions

The Grothendieck programme

The approximation property

Mapping spaces

Absolutely summing mappings

Local theory and integrality

Local reflexivity, exactness, and nuclearity

Local reflexivity and exact integrality

Some algebraic applications

Noncommutative harmonic analysis

An abstract characterization for nonselfadjoint operator algebras

Preliminaries