On the Hereditary Properties of Triangular Banach Algebras in Terms of Module Arens Regularity

Abstract

The present paper is the first attempt to investigate ‏‎the h‎ereditary propertie‏s between triangular Banach algebras and their corner Banach algebras in terms of module Arens regularity.‎ For this purpose, we will examine the conditions under which ‎the ‎‎module Arens regularity of triangular Banach algebra ‎‎$‎\mathcal{T}=\Mat{\mathcal A}{\mathcal M}{\mathcal B}$‎ is obtained from ‎the ‎‎module Arens regularity of the corner algebras $\mathcal A$ and $\mathcal B$.