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.

Cited by in corpus (6)

• A non-amenable groupoid whose maximal and reduced $C^{\ast }$-algebras are the same
• Some remarks about the weak containment property for groupoids and semigroups
• Amenability and weak containment for actions of locally compact groups on $C^{\ast }$-algebras
• Properness conditions for actions and coactions
• Nuclearity for partial crossed products by exact discrete groups
• Non-supramenable groups acting on locally compact spaces