Journal of Operator Theory
Volume 80, Issue 1, Summer 2018 pp. 167-185.
The orbit spaces of groupoids whose $C^*$-algebras are GCR
Authors:
Daniel W. van Wyk
Author institution: Department of Mathematics and Statistics, University of Otago,
Dunedin, 9010, New Zealand
Summary: Let $G$ be a second countable locally compact Hausdorff groupoid
with a continuous Haar system. We remove the assumption of amenability in a theorem by
Clark about GCR groupoid $C^*$-algebras. We show that if the groupoid
$C^*$-algebra of $G$ is GCR then the orbit space of $G$ is a $T_0$ topological
space.
DOI: http://dx.doi.org/10.7900/jot.2017sep11.2185
Keywords: groupoids, $C^*$-algebras, type I representations, GCR, postliminal
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