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

Abstract

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.

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• Nuclearity for partial crossed products by exact discrete groups