Generalized almost periodicity in groups

Abstract

A module of almost periodic functions on a group is closed with respect to a quite general seminorm. The new space of functions is characterized in terms of the internal properties of its members. This yields new characterizations of Besicovitch and Weyl almost periodic functions in a variety of group-theoretic settings. Eberlein’s theorem that weakly almost periodic functions on the real line are Weyl almost periodic is extended to locally compact groups.