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

Abstract

We prove that the crossed product Banach algebra ${\ell }^1(A,G,\alpha )$ 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 commutative or finite dimensional ${\mathrm{C}}^{\ast }$-algebra. Perspectives for further developments are indicated.

Improved discussion of the relation with the existing literature and of perspectives for further developments. 8 pages. To appear in Integral Equations and Operator Theory

References in corpus (1)

• Algebraically irreducible representations and structure space of the Banach algebra associated with a topological dynamical system

Cited by in corpus (3)

• Applications of amenable semigroups in operator theory
• Stable rank for inclusions of Banach algebras
• On the continuity of intertwining operators over generalized convolution algebras