**Translations of Mathematical Monographs**

2005;
202 pp;
Hardcover

MSC: Primary 46;

Print ISBN: 978-0-8218-3810-5

Product Code: MMONO/226

List Price: $94.00

AMS Member Price: $75.20

MAA Member Price: $84.60

**Electronic ISBN: 978-1-4704-4650-5
Product Code: MMONO/226.E**

List Price: $94.00

AMS Member Price: $75.20

MAA Member Price: $84.60

#### Supplemental Materials

# Hilbert \(C^{*}\)-Modules

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*V. M. Manuilov; E. V. Troitsky*

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 (self-duality, 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.

#### Readership

Graduate students and research mathematicians interested in functional analysis and operator algebras.

#### Table of Contents

# Table of Contents

## Hilbert $C^{*}$-Modules

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Basic definitions 110
- Operators on Hilbert modules 1524
- Hilbert modules over ๐*-algebras 5564
- Reflexive Hilbert ๐ถ*-modules 7584
- Multipliers of ๐ด-compact operators. Structure results 99108
- Diagonalization of operators over ๐ถ*-algebras 133142
- Homotopy triviality of groups of invertible operators 159168
- Hilbert modules and ๐พ๐พ-theory 181190
- Bibliography 193202
- Notation index 199208
- Index 201210
- Back Cover Back Cover1214