The Rajchman algebra B-0(G) of a locally compact group G

Abstract

Let G be a locally compact group, B(G) the Fourier-Stieltjes algebra of G and B-0(G) = B(G) boolean and C-0(G). The space B-0(G) is a closed ideal of B(G). In this paper, we study the Banach algebra B-0(G) under various aspects. The main emphasis is on regularity and the existence of various kinds of approximate identities, the question of when the quotient of B-0(G) modulo the Fourier algebra A(G) is radical, the Bochner-Schoenberg-Eberlein property and a characterization of elements in B-0(G) in terms of continuity of translation properties. The paper also contains a number of illustrating examples.