2010/10/27 by Kazem Haghnejad Azar, Azar, Kazem Haghnejad
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA
paper · pdf · doi:10.48550/arxiv.1010.5688
arxiv created 2010/10/27 · arxiv updated 2010/10/28
For Banach left and right module actions, we extend some propositions from Lau and Ulger into general situations and we establish the relationships between topological centers of module actions. We also introduce the new concepts as Lw^*w-property and Rw^*w-property for Banach A-bimodule B and we obtain some conclusions in the topological center of module actions and Arens regularity of Banach algebras. we also study some factorization properties of left module actions and we find some relations of them and topological centers of module actions. For Banach algebra A, we extend the definition of ∗-involution algebra into Banach A-bimodule B with some results in the factorizations of B^*. We have some applications in group algebras.