Strong pure infiniteness of crossed products
Strong pure infiniteness of crossed products
Consider an exact action of discrete group $G$ on a separable $C^*$-algebra $A$. It is shown that the reduced crossed product $A\rtimes_{\sigma, \lambda} G$ is strongly purely infinite - provided that the action of $G$ on any quotient $A/I$ by a $G$-invariant closed ideal $I\neq A$ is element-wise properly outer …