THE ANALOGUE OF WEIGHTED GROUP ALGEBRA FOR SEMITOPOLOGICAL SEMIGROUPS

In [1,2,3], A. C. Baker and J.W. Baker studied the subspace Ma(S) of the convolution measure algebra M, (S) of a locally compact semigroup. H. Dzinotyiweyi in [5,7] considers an analogous measure space on a large class of C-distinguished topological semigroups containing all completely regular topological semigroups. In this paper, we extend the definitions to study the weighted semigroup algebra Ma (S, o), where o is a weight function on a Cdistinguished semitopological semigroup S. We will show that this subspace is a convolution measure algebra. As acorollary, this answers in the affirmative a question raised by J.W. Baker and H. Dzinotyiweyi in [6]