Fourier–Stieltjes algebras and measure algebras on compact right topological groups.

Abstract: Let G be an admissible compact Hausdorff right topological group, that is, a group with a Hausdorff topology such that for each , the map is continuous, and the set of such that the map is continuous is dense in G. Such groups arise in the study of distal flows. In this paper we study the Fourier–Stieltjes algebra , the linear span of the continuous positive definite functions on G. We show that 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 -fixed point properties on . We also study some related properties on the measure algebra . [Copyright &y& Elsevier]