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THE CROSSED PRODUCT BY A POINTWISE UNITARY ACTION ON A C*-ALGEBRA WITH CONTINUOUS TRACE

Published online by Cambridge University Press:  20 January 2009

Klaus Deicke
Klaus Deicke
Affiliation:
Universität-Gesamthochschule Paderborn, Fachbereich Mathematik-Informatik, Warburger Stra{\ss}e 100, D-33095 Paderborn, DE ([email protected])
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Abstract

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Let $G$ be a locally compact group, $A$ a continuous trace $C^*$-algebra, and $\alpha$ a pointwise unitary action of $G$ on $A$. It is a result of Olesen and Raeburn that if $A$ is separable and $G$ is second countable, then the crossed product $A\times_\alpha G$ has continuous trace. We present a new and much more elementary proof of this fact. Moreover, we do not even need the separability assumptions made on $A$ and $G$.

AMS 2000 Mathematics subject classification: Primary 46L55

Keywords

continuous trace $C^*$-algebraactioncrossed productpointwise unitary
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 1 , February 2001 , pp. 215 - 218
Copyright
Copyright © Edinburgh Mathematical Society 2001