Amenability of the Algebras R(S), F(S) of a Topological Semigroup S

For a locally compact Hausdorff semigroup S, the $L^{\mathrm{\infty }}$ representation algebra R(S) was extensively studied by Dunkl and Ramirez. The Fourier-Stieltjes algebra F(S) of a topological semigroup was studied by Lau. The aim of this paper is to investigate these two algebras and study the amenability of them with respect to the structure of S.