Arens Regularity And Factorization Property
Kazem Haghnejad Azar

TL;DR
This paper explores the Arens regularity and topological center properties of module actions in Banach algebras, extending existing concepts and establishing relationships between dual spaces, module actions, and tensor products.
Contribution
It extends the study of topological centers from Banach algebra duals to module actions, providing new relationships and conditions for Arens regularity in Banach modules and tensor products.
Findings
Established relationships between topological centers of duals and module actions.
Proved conditions under which the topological center equals the entire space.
Analyzed Arens regularity of tensor products of Banach algebras.
Abstract
In this paper, we will study some Arens regularity properties of module actions. Let be a Banach and let and be the topological centers of the left module action and the right module action , respectively. In this paper, we will extend some problems from topological center of second dual of Banach algebra , , into spaces and . We investigate some relationships between and topological centers of module actions. For an unital Banach we show that and as results in group algebras, for locally compact group , we have…
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topology and Set Theory
