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Strength of convergence in non-free transformation groups

By Robert Archbold and Astrid an Huef

Abstract

AbstractLet (G,X) be a transformation group where the group G does not necessarily act freely on the space X. We investigate the extent to which the action of G may fail to be proper. Stability subgroups are used to define new notions of strength of convergence in the orbit space and of measure accumulation along orbits. By using the representation theory of the associated crossed product C⁎-algebra, we show that these notions are equivalent under certain conditions

Publisher: Elsevier Inc. Published by Elsevier Inc.
Year: 2012
DOI identifier: 10.1016/j.jfa.2012.05.005
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