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]