Hilbert $C^{*}$-Modules
( Translations of Mathematical Monographs )
Publication series ： Translations of Mathematical Monographs
Author： V. M. Manuilov;E. V. Troitsky
Publisher： American Mathematical Society
Publication year： 2018
E-ISBN: 9781470446505
P-ISBN(Paperback): 9780821838105
Subject： O177.5 Banach algebras; Normed algebras (), algebraic topology, abstract harmonic analysis
Keyword： 数学
Language： ENG
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Hilbert $C^{*}$-Modules
Description
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, in index theory of elliptic operators, in $K$- and $KK$-theory, and in noncommutative geometry as a whole. Alongside these applications, the theory of Hilbert $C^*$-modules is interesting on its own. The present book is an introduction to the theory of Hilbert $C^*$-modules. 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.
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