Buch, Englisch, 202 Seiten, Gewicht: 604 g
Buch, Englisch, 202 Seiten, Gewicht: 604 g
Reihe: Translations of Mathematical Monographs
ISBN: 978-0-8218-3810-5
Verlag: American Mathematical Society
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.
