Vrej Zarikian. Source: Annals of Functional Analysis, Volume 10, Number 1, 60--71.Abstract:
Let $G$ be a discrete group acting on a unital $C^{*}$ -algebra $\mathcal{A}$ by $*$ -automorphisms. We characterize (in terms of the dynamics) when the inclusion $\mathcal{A}\subseteq\mathcal{A}\rtimes_{r}G$ has a unique conditional expectation, and when it has a unique pseudoexpectation in the sense of Pitts; we do likewise for the inclusion $\mathcal{A}\subseteq\mathcal{A}\rtimes G$ . As an application, we re-prove (and potentially extend) some known $C^{*}$ -simplicity results for $\mathcal{A}\rtimes_{r}G$ .