Isomorphisms of Multiplier Algebras

Abstract

Suppose that G1 and G2 are two locally compact Hausdorff groups with identity elements e and e’ and with respective left Haar measures dx and dy. Let 1 ≦ p ≦ ∞, and Lp(Gi) be the usual Lebesgue space over Gi formed relative to left Haar measure on Gi. We denote by M(Gi) the space of Radon measures, and by Mbd(Gi) the space of bounded Radon measures on Gi. If a ϵ Gi we write ϵa for the Dirac measure at the point a. Cc(Gi) will denote the space of continuous, complex-valued functions on Gi with compact supports, whilst Cc+ (Gi) will denote that subset of Cc(Gi) consisting of those functions which are real-valued and non-negative.