On the Functorial Properties of the p-Analog of the Fourier–Stieltjes Algebras

Abstract

In this paper, some known results about the functorial properties of the Fourier–Stieltjes algebra, B(G), will be generalized. First of all, the idempotent theorem on the Fourier–Stieltjes algebra will be promoted and linked to the p-analog one. Next, the p-analog of the \(\pi\)-Fourier space introduced by Arsac will be given, and by taking advantage of the theory of ultrafilters, the connection between the dual space of the algebra of p-pseudofunctions and the p-analog of the \(\pi\)-Fourier space will be fully investigated. As the main result, one of the significant and applicable functorial properties of the p-analog of the Fourier–Stieltjes algebras will be achieved.