Weighted function algebras on groups and semigroups

Abstract

For a locally compact topological group admitting a weight function, we establish necessary and sufficient criteria for all the weighted continuous functions to be weakly almost periodic. Among other results, we show that weak almost periodicity of all ω-weighed continuous functions on a discrete semigroup S, can be very different drom the phenomenon of regularity of multiplication in the weighted algebra ℓ1 (S, w).