Isomorphisms of Multiplier Algebras

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.