Herz-Schur Multipliers of Fell Bundles

Abstract

In this paper we develop the notion of Herz-Schur multipliers to the context of Fell bundle, and we give a necessary and sufficient condition if the reduced cross-sectional $C^{\ast }$-algebra $C_r^{\ast }(\mathfrak{B})$ of Fell bundle $\mathfrak{B}$ over discrete group $G$ is nuclear in terms of this generalized notion. As an application, we prove that if $C_r^{\ast }(\mathfrak{B})$ is nuclear, then for any subgroup $H\subset G$, the $C^{\ast }$-algebra $C_r^{\ast }({\mathfrak{B}}_H)$ is nuclear.

Cited by in corpus (1)

• Amenability, Nuclearity and Tensor Products of $C^{\ast }$-Algebraic Fell Bundles under the Unified Viewpoint of the Fell-Doran Induced Representation Theory