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arXiv · 1705.02623

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

Marcel de Jeu·Rachid El Harti·Paulo R. Pinto
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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.

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Marcel de Jeu, Rachid El Harti, Paulo R. Pinto. 2017-05-07. Amenable crossed product Banach algebras associated with a class of $\mathrm{C}^\ast$-dynamical systems. II. https://arxiv.org/abs/1705.02623

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