On the topological centers of Banach algebras

Abstract

Let A be a Banach algebra with a bounded approximate identity. Let $Z_2$ and $widetilde{Z}_2$ be respectively, the topological centers of the algebras A** and (AA*)* with respect to the second Arens multiplication. In this paper, we show that $widetilde{M}_2$ is isometrically isomorphic to LM (A)> where $widetilde{M}_2$ is a closed subalgebra of $widetilde{Z}_2$ and LM(A) is the set of left multipliers operators of the Banach algebra A.