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Journal of Operator Theory

Volume 72, Issue 1, Summer 2014  pp. 41-47.

A characterization of amenability of group actions on $C^\ast$-algebras

Authors:  Masayoshi Matsumura
Author institution: Department of Mathematical Science, University of Tokyo, Komaba, 153-8914, Japan

Summary: We show that coincidence of the full and reduced crossed product $C^\ast$-algebras of a group action on a unital commutative $C^\ast$-algebra implies amenability of the action whenever the group is exact. This is a partial answer to a problem posed by C. Anantharaman-Delaroche in 1987.

Keywords: $C^\ast$-algebra, amenable action, exact group

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