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

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.