Norming in Discrete Crossed Products

TL;DR

This paper establishes conditions under which the inclusion of a unital C*-algebra into its reduced crossed product by a discrete group is norming, with implications for separable or simple algebras with unique pseudo-expectations.

Contribution

It provides two new dynamical criteria ensuring the norming property for C*-inclusions in crossed products, extending understanding of their structure.

Findings

Identifies conditions for norming in crossed product inclusions.

Shows that separable or simple algebras with a unique pseudo-expectation satisfy norming.

Connects dynamical properties with operator algebraic structure.

Abstract

Let $G \curvearrowright A$ be an action of a discrete group on a unital $C^*$-algebra by $*$-automorphisms. In this note, we give two sufficient dynamical conditions for the $C^*$-inclusion $A \subseteq A \rtimes_r G$ 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 $A \subseteq A \rtimes_r G$ is norming provided it has a unique pseudo-expectation in the sense of Pitts.