New Concepts on Module Arens Regularity for Module Banach Algebras - Omid Pourbahri Rahpeyma; Davood Ebrahimi Bagha; Ghasem Soleimani Rad (Journal of Mathematics)
The main purpose of this paper is to introduce a new definition of JA-module Arens regularity, which extends former standard definition. Then a new module structure on the semigroup algebra l1S as l1ES-module with nontrivial right and left module actions is constructed. Using this construction, it is also proved that l1S is a Jl1S-module Arens regular if and only if S/≈ is finite.