We give a characterization of the ”uniform closure” of the dual of a C-algebra. Some applications in harmonic analysis are given. 1. Four topologies on the unit ball of a C-algebra Let A be a C-algebra and P (A),S(A),A1, and A denote the pure state space, state space, closed dual unit ball, and the dual of A, respectively, all equipt with the w-topology. Let A1denote the closed unit ball of A. ...
