0. Introduction. In this paper two commutative, semisimple Banach algebras with involution, viz., A(G) and B(G), (called the Fourier algebra of G and the Fourier-Stieltjes algebra of G, respectively) are defined (as in [5]) for an arbitrary locally compact topological group G. [Note. As algebras A(G) and B(G) are subalgebras of the algebra of bounded continuous functions on G.] The main purpose...