C*-Algebras by Example

Released on by Kenneth R. Davidson
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  • C*-Algebras by Example Book Detail

  • Author : Kenneth R. Davidson
  • Release Date : 2023-10-04
  • Publisher : American Mathematical Society, Fields Institute
  • Genre : Mathematics
  • Pages : 325
  • ISBN 13 : 1470475081
  • File Size : 32,32 MB
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C*-Algebras by Example by Kenneth R. Davidson PDF Summary

Book Description: The subject of C*-algebras received a dramatic revitalization in the 1970s by the introduction of topological methods through the work of Brown, Douglas, and Fillmore on extensions of C*-algebras and Elliott's use of $K$-theory to provide a useful classification of AF algebras. These results were the beginning of a marvelous new set of tools for analyzing concrete C*-algebras. This book is an introductory graduate level text which presents the basics of the subject through a detailed analysis of several important classes of C*-algebras. The development of operator algebras in the last twenty years has been based on a careful study of these special classes. While there are many books on C*-algebras and operator algebras available, this is the first one to attempt to explain the real examples that researchers use to test their hypotheses. Topics include AF algebras, Bunce–Deddens and Cuntz algebras, the Toeplitz algebra, irrational rotation algebras, group C*-algebras, discrete crossed products, abelian C*-algebras (spectral theory and approximate unitary equivalence) and extensions. It also introduces many modern concepts and results in the subject such as real rank zero algebras, topological stable rank, quasidiagonality, and various new constructions. These notes were compiled during the author's participation in the special year on C*-algebras at The Fields Institute for Research in Mathematical Sciences during the 1994–1995 academic year. The field of C*-algebras touches upon many other areas of mathematics such as group representations, dynamical systems, physics, $K$-theory, and topology. The variety of examples offered in this text expose the student to many of these connections. Graduate students with a solid course in functional analysis should be able to read this book. This should prepare them to read much of the current literature. This book is reasonably self-contained, and the author has provided results from other areas when necessary.

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C*-Algebras by Example

C*-Algebras by Example

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The subject of C*-algebras received a dramatic revitalization in the 1970s by the introduction of topological methods through the work of Brown, Douglas, and Fi

C*-Algebras by Example

C*-Algebras by Example

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An introductory graduate level text presenting the basics of the subject through a detailed analysis of several important classes of C*-algebras, those which ar

C*-Algebras and Operator Theory

C*-Algebras and Operator Theory

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This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and phy