C*-Algebras by Example (Fields Institute Monographs, 6) - Hardcover

Kenneth R. Davidson

Hardcover

ISBN 10: 0821805991 ISBN 13: 9780821805992

Publisher: Amer Mathematical Society, 1996

Synopsis

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. <P>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. <P>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.

About this title

Review

"The book ... occupies a special place among numerous textbooks and monographs as in the subject chosen by the author so also in the method of presentation of the material ... Each chapter contains numerous interesting exercises ... can be recommended as a good introduction in the theory of $C^*$-theory for all who are not yet under the charm of this remarkable theory as well as for specialists in the field as a collection of useful and carefully selected tools and methods ... useful for numerous lectures as a textbook for special courses with different aspects of $C^*$-algebras." ---- Zentralblatt MATH

"Altogether, a very commendable introduction and collection." ---- Monatshefte für Mathematik

"One can assign parts of Davidson's book to good students learning the subject and expect good results ... the details persist even when the going gets tough ... this is the only book I know in which one can go through the BDF classification of essentially normal operators and follow, point by point, to the end." ---- Bulletin of the AMS

Edition details

• Publisher: Amer Mathematical Society
• Publication date: 1996
• Language: English
• ISBN 10: 0821805991
• ISBN 13: 9780821805992
• Binding: Hardcover
• Number of pages: 309