Isomorphisms of some convolution algebras and their multiplier algebras

Abstract

Let G1 and G2 be two locally compact abelian groups and let 1 ≤ p ∞. We prove that G1 and G2 are isomorphic as topological groups provid∈d there exists a bipositive or isometric algebra isomorphism of M(Ap (G1)) onto M(Ap (G2)). As a consequence of this, we prove that G1 and G2 are isomorphic as topological groups provided there exists a bipositive or isometric algebra isomorphism of Ap (G1) onto Ap (G2). Similar results about the algebras L1 ∩ Lp and L1 ∩ C0 are also established.