Arens Regularity of Certain Class of Banach Algebras

Abstract

We study Arens regularity of the left and right module actions of 𝐴 on 𝐴(𝑛), where 𝐴(𝑛) is the nth dual space of a Banach algebra 𝐴, and then investigate (quotient) Arens regularity of 𝑈=𝐴⊕𝐴(𝑛) as a module extension of Banach algebras.