Arens Regularity of Projective Tensor Product

Abstract

In this paper, we study approximate identity properties, some propositions from Baker, Dales, Lau in general situations and we establish some relationships between the topological centers of module actions and factorization properties with some results in group algebras. We consider under which sufficient and necessary conditions the Banach algebra $A\widehat{\otimes}B$ is Arens regular.