The Rajchman algebra B0(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 ) ∩ 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.