A note on the $p$-operator space structure of the $p$-analog of the Fourier-Stieltjes algebra

TL;DR

This paper introduces and studies a specific $p$-operator space structure for the $p$-analog of the Fourier-Stieltjes algebra, linking it to the algebra of universal $p$-pseudofunctions and exploring related problems.

Contribution

It presents a new $p$-operator space structure for the $p$-analog of the Fourier-Stieltjes algebra derived from its predual, expanding the understanding of its operator space properties.

Findings

Defined a $p$-operator space structure from the predual

Proved some applicable and expected results

Opened new questions in the study of $p$-analog Fourier-Stieltjes algebras

Abstract

In this paper one of the possible $p$-operator space structures of the $p$-analog of the Fourier-Stieltjes algebra will be introduced, and to some extend will be studied. This special sort of operator structure will be given from the predual of this Fourier type algebra, that is the algebra of universal $p$-pseudofunctions. Furthermore, some applicable and expected results will be proven. Current paper can be considered as a new gate into the collection of problems around the $p$-analog of the Fourier-Stieltjes algebra, in the $p$-operator space structure point of view.