Multipliers for certain convolution measure algebras

Abstract

Let (A,*) be a commutative semisimple convolution measure algebra with structure semigroup I", and let S denote a commutative locally compact topological semigroup.Under the assumption that A possesses a weak bounded approximate identity, it is shown that there is a topological embedding of the multiplier algebra ^A[{A) of A in A/(r).This representation leads to a proof of the commutative case of Wendel's theorem for A = L\(G), where G is a commutative locally compact topological group.It is also proved that if I, (S) has a weak bounded approximate identity of norm one, then H(l,(S)) is isometrically isomorphic to /,((S)), where 0(5) is the multiplier semigroup of S. Likewise, if S is cancellative, then <M,h(S)) is isometrically isomorphic to l((S)).An example is provided of a semigroup 5 for which /,((S)) is isomorphic to a proper subset of <Jt(lt(S)).