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Hardcover ISBN:  9780821838105 
Product Code:  MMONO/226 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470446505 
Product Code:  MMONO/226.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821838105 
eBook ISBN:  9781470446505 
Product Code:  MMONO/226.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 226; 2005; 202 ppMSC: Primary 46
Based on lectures delivered by the authors at Moscow State University, this volume presents a detailed introduction to the theory of Hilbert \(C^*\)modules.
Hilbert \(C^*\)modules provide a natural generalization of Hilbert spaces arising when the field of scalars \(\mathbf{C}\) is replaced by an arbitrary \(C^*\)algebra. The general theory of Hilbert \(C^*\)modules appeared more than 30 years ago in the pioneering papers of W. Paschke and M. Rieffel and has proved to be a powerful tool in operator algebras theory, index theory of elliptic operators, \(K\) and \(KK\)theory, and in noncommutative geometry as a whole. Alongside these applications, the theory of Hilbert \(C^*\)modules is interesting on its own.
In this book, the authors explain in detail the basic notions and results of the theory, and provide a number of important examples. Some results related to the authors' research interests are also included. A large part of the book is devoted to structural results (selfduality, reflexivity) and to nonadjointable operators.
Most of the book can be read with only a basic knowledge of functional analysis; however, some experience in the theory of operator algebras makes reading easier.
ReadershipGraduate students and research mathematicians interested in functional analysis and operator algebras.

Table of Contents

Chapters

Basic definitions

Operators on Hilbert modules

Hilbert modules over $W^*$algebras

Reflexive Hilbert $C^*$modules

Multipliers of $A$compact operators. Structure results

Diagonalization of operators over $C^*$algebras

Homotopy triviality of groups of invertible operators

Hilbert modules and $KK$theory


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Based on lectures delivered by the authors at Moscow State University, this volume presents a detailed introduction to the theory of Hilbert \(C^*\)modules.
Hilbert \(C^*\)modules provide a natural generalization of Hilbert spaces arising when the field of scalars \(\mathbf{C}\) is replaced by an arbitrary \(C^*\)algebra. The general theory of Hilbert \(C^*\)modules appeared more than 30 years ago in the pioneering papers of W. Paschke and M. Rieffel and has proved to be a powerful tool in operator algebras theory, index theory of elliptic operators, \(K\) and \(KK\)theory, and in noncommutative geometry as a whole. Alongside these applications, the theory of Hilbert \(C^*\)modules is interesting on its own.
In this book, the authors explain in detail the basic notions and results of the theory, and provide a number of important examples. Some results related to the authors' research interests are also included. A large part of the book is devoted to structural results (selfduality, reflexivity) and to nonadjointable operators.
Most of the book can be read with only a basic knowledge of functional analysis; however, some experience in the theory of operator algebras makes reading easier.
Graduate students and research mathematicians interested in functional analysis and operator algebras.

Chapters

Basic definitions

Operators on Hilbert modules

Hilbert modules over $W^*$algebras

Reflexive Hilbert $C^*$modules

Multipliers of $A$compact operators. Structure results

Diagonalization of operators over $C^*$algebras

Homotopy triviality of groups of invertible operators

Hilbert modules and $KK$theory