The higher duals of certain class of Banach algebras

Abstract

Given a Banach space $A$ and fix a non-zero $\phi \in A^{\ast }$ with $\Vert \phi \Vert \le 1$. Then the product $a\cdot b=⟨\phi ,a⟩b$ turning $A$ into a Banach algebra which will be denoted by ${}_{\phi }A.$ Some of the main properties of ${}_{\phi }A$ such as Arens regularity, $n$-weak amenability and semi-simplicity are investigated.

6 pages