Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-27T22:34:00.508Z Has data issue: false hasContentIssue false
  • English
  • Français

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 (deicke@uni-paderborn.de)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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