A strict topology on Orlicz spaces

Abstract

Let ϕ be a Young function, Ω be a locally compact space, and μ be a positive Radon measure on Ω. We consider a strict topology βϕ (in the sense of Sentilles-Taylor) on the Orlicz function space Mϕ(Ω) and investigate various properties of this locally convex topology. We also study the Orlicz space Mϕ(G) of a locally compact group G with a left Haar measure under the strict topology βϕ and certain other natural locally convex topologies. Finally we present some results on various continuity properties of convolution operators on Mϕ(G) under the βϕ topology and other natural ones