Amenable crossed product Banach algebras associated with a class of ${\mathrm{C}}^{\ast }$-dynamical systems. II

Abstract

We prove that the crossed product Banach algebra ${\ell }^1(G,A;\alpha )$ that is associated with a ${\mathrm{C}}^{\ast }$-dynamical system $(A,G,\alpha )$ is amenable if $G$ is a discrete amenable group and $A$ is a strongly amenable ${\mathrm{C}}^{\ast }$-algebra. This is a consequence of the combination of a more general result with Paterson's characterisation of strongly amenable unital ${\mathrm{C}}^{\ast }$-algebras in terms of invariant means for their unitary groups.

19 pages