Norming in Discrete Crossed Products

Abstract

Let $G\curvearrowright A$ be an action of a discrete group on a unital $C^{\ast }$-algebra by $\ast$-automorphisms. In this note, we give two sufficient dynamical conditions for the $C^{\ast }$-inclusion $A\subseteq A{⋊}_{r}G$ to be norming in the sense of Pop, Sinclair, and Smith. As a consequence of our results, when $A$ is separable or simple, the inclusion $A\subseteq A{⋊}_{r}G$ is norming provided it has a unique pseudo-expectation in the sense of Pitts.

27 pages, 2 figures