On the continuity of automorphic representations of groups

Abstract

Given a weakly continuous automorphic representation α of a groupG on a concreteC*-algebra$\mathfrak{A}$, we show that a mild joint continuity condition makes it possible to extend α to a weakly continuous representation ofG on the weak closure of$\mathfrak{A}$. IfG is locally compact and$\mathfrak{A}$ is a von Neumann algebra, this condition is automatically satisfied.