Amenable crossed product Banach algebras associated with a class of C^∗-dynamical systems. II

2017/05/07 by Marcel de Jeu, de Jeu, Marcel, Rachid El Harti +3
Mathematics · #46H25 #46L55 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 47L65 #Secondary 43A07

paper · pdf · doi:10.48550/arxiv.1705.02623

openalex publication_date 2017/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the crossed product Banach algebra ℓ¹(G,A;α) that is associated with a \mathrm C^∗-dynamical system (A,G,α) is amenable if G is a discrete amenable group and A is a strongly amenable \mathrm C^∗-algebra. This is a consequence of the combination of a more general result with Paterson's characterisation of strongly amenable unital C^∗-algebras in terms of invariant means for their unitary groups.

Related

• Crossed products of Banach algebras. I
• Hermitian crossed product Banach algebras
• Weak amenability for dynamical systems
• Dynamical systems of type (m,n) and their C*-algebras
• Perturbations of crossed product C*-algebras by amenable groups