Hilbert $C*$-Modules

Erscheinungsjahr 2005
ISBN: 978-0-8218-3810-5
Verlag: American Mathematical Society

Buch, Englisch, 202 Seiten, Gewicht: 604 g

Reihe: Translations of Mathematical Monographs

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.

Contents

- 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

- Bibliography

- Notation index

- Index

Zielgruppe

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

Autoren/Hrsg.

Manuilov, V. M.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Über Autor(innen)

Manuilov, Moscow State University, Russia and Troitsky, Moscow State University, Russia