On the density of the Fourier–Stieltjes algebra

Abstract

Let G be a locally compact group and 1<p<∞. Let Ap(G) denote the Figà-Talamanca–Herz algebra and MAp(G) its pointwise multiplier algebra. In this paper, we shall introduce two new spaces of multipliers of Ap(G), defined as coefficient functions of certain representations of G on some interpolation couples. Then we shall show that, in the amenable case, the Fourier–Stieltjes algebra B(G) is dense in MAp(G), and that MAp(G), as an ordered space, is a complete invariant for G.