A strict topology on Orlicz spaces

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.