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 β φ (in the sense of Sentilles‐Taylor) on the Orlicz function spaceM φ ( Ω )and investigate various properties of this locally convex topology. We also study the Orlicz spaceM φ ( G )of a locally compact group G with a left Haar measure under the strict topology β φ and certain other natural locally convex topologies. Finally we present some results on various continuity properties of convolution operators onM φ ( G )under the β φ topology and other natural ones.