Isomorphisms of some Segal algebras and their multiplier algebras

Abstract

Let G1, G2, be locally compact groups and let S1, S2, be Segal algebras on G1, G2, respectively. Under certain conditions on G1, G2, and S1, S2, we prove that if there is a bipositive or isometric isomorphism between S1, S2, or between their multiplier algebras then G1, and G2, are topologically isomorphic.