Fourier-Stieltjes algebras and measure algebras on compact right topological groups

Let G be an admissible compact Hausdorff right topological group, that is, a group with a Hausdorff topology such that for each a∈G, the map gga is continuous, and the set of a∈G such that the map gag is continuous is dense in G. Such groups arise in the study of distal flows. In this paper we study the Fourier-Stieltjes algebra B(G), the linear span of the continuous positive definite functions on G. We show that B(G) is isomorphic with the Fourier-Stieltjes algebra of an associated compact topological group. This result is then applied to obtain some geometric properties including the weak and weak^*-fixed point properties on B(G). We also study some related properties on the measure algebra M(G).