Hilbert C*-modules

Released on by Vladimir Markovich Manuĭlov
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  • Hilbert C*-modules Book Detail

  • Author : Vladimir Markovich Manuĭlov
  • Release Date :
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 216
  • ISBN 13 : 9780821889664
  • File Size : 41,41 MB
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Hilbert C*-modules by Vladimir Markovich Manuĭlov PDF Summary

Book Description: 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 inoperator 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 thetheory, 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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