On multipliers of Segal algebras

Abstract

Let T be a multiplier of a Segal algebra S on a locally compact abelian group G. We prove that T 2 ( S ) {T^2}(S) is closed if and only if T is a product of an idempotent and an invertible multiplier. We also show that the techniques developed in the proof of this theorem can be used to obtain some other known results.