Continuity of Convolution and SIN Groups

Abstract

AbstractLet the measure algebra of a topological group G be equipped with the topology of uniform convergence on bounded right uniformly equicontinuous sets of functions. Convolution is separately continuous on the measure algebra, and it is jointly continuous if and only if G has the SIN property. On the larger space LUC(G)*, which includes the measure algebra, convolution is also jointly continuous if and only if the group has the SIN property, but not separately continuous for many non-SIN groups.