K-Theory and C*-Algebras: A Friendly Approach

Hardcover | November 1, 1990

byN. E. Wegge-Olsen

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K-theory is often considered a complicated `specialist's' theory. This book is an introduction to the basics and provides detailed explanation of the various concepts required for a deeper understanding of the subject. Some familiarity with basic C*algebra theory is assumed and then followsa careful construction and analysis of the operator K-theory groups and proof of the results of K-theory, including Bott periodicity. Of specific interest to algebraists and geometrists, the book aims to give full instruction. No details are left out in the presentation and many instructive and generously hinted exercises are provided. Apart from K-theory, this book offers complete and self contained expositions of important advanced C*-algebraic constructions like tensor products, multiplier algebras and Hilbert modules.

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From the Publisher

K-theory is often considered a complicated `specialist's' theory. This book is an introduction to the basics and provides detailed explanation of the various concepts required for a deeper understanding of the subject. Some familiarity with basic C*algebra theory is assumed and then followsa careful construction and analysis of the o...

N. E. Wegge-Olsen is at Universitetsparken, 2100 Copenhagen.
Format:HardcoverDimensions:382 pages, 9.21 × 6.14 × 1.02 inPublished:November 1, 1990Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198596944

ISBN - 13:9780198596943

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Table of Contents

General notationIntroductionPart I: C*-algebras1. C*-algebras - a summary2. Multiplier algebras3. Extensions of C*-algebras4. Invertibles and unitaries5. ProjectionsPart II: Fundamentals of K-Theory6. K0-basic properties7. K1 and suspensions8. The index map in K-theory9. Bott periodicity10. K-theory for multiplier algebras11. Homology12. Some examples: AF-algebras, Cuntz algebras, rotation algebras13. Vector bundles and topological K-theoryPart III: Hilbert Modules and a Generalized Index Theory14. The classical Fredholm index15. Hilbert modules16. The Kuiper-Mingo theorem17. A generalized Fredholm indexPart IV: AppendicesG. The Grothendieck groupL. Inductive limitsO. (Dis)order and positivity in C*-algebrasT. Tensor products -or: the importance of being subcrossReferencesSubject index

Editorial Reviews

`... it is written in a very lively and user friendly style... Altogether I think this book is very recommendable as a first introduction to the subject.'Monatshefte fur Mathematik, 3 April 1995