On the Topological Centers of Banach Algebras

Let A be a Banach algebra with a bounded approximate identity. Let   and be respectively, the topological centers of the algebras A** and insert ignore into journalissuearticles values(AA*);* with respect to the second Arens multiplication. In this paper, we show that is isometrically isomorphic to LMinsert ignore into journalissuearticles values(A); , where   is a closed subalgebra of and LMinsert ignore into journalissuearticles values(A); is the set of left multipliers operators of the Banach algebra A.   Key words: Topological center, Arens multiplication, Banach algebra, Left multiplier operator