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The Toeplitz operator proof of noncommutative Bott periodicity

Part of: Selfadjoint operator algebras Topological (rings and) algebras with an involution $K$-theory and operator algebras

Published online by Cambridge University Press:  09 April 2009

N. Christopher Phillips
N. Christopher Phillips
Affiliation:
University of GeorgiaAthens, GA 30602, USA
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Abstract

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We adapt the Toeplitz operator proof of Bott periodicity to give a short direct proof of Bott periodicity for the representable K-theory of σ-C*-algebras. We further show how the use of this proof and the right definitions simplifies the derivation of the basic properties of representable K-theory.

MSC classification

Secondary: 19K99: None of the above, but in this section 46K99: None of the above, but in this section 46L80: $K$-theory and operator algebras (including cyclic theory)

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 2 , October 1992 , pp. 229 - 251
Copyright
Copyright © Australian Mathematical Society 1992

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