On the density of the Fourier–Stieltjes algebra

Let G be a locally compact group and 1 < p < ∞ . Let A p ( G ) denote the Figà-Talamanca–Herz algebra and MA p ( G ) its pointwise multiplier algebra. In this paper, we shall introduce two new spaces of multipliers of A p ( 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 MA p ( G ) , and that MA p ( G ) , as an ordered space, is a complete invariant for G .