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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