APPROXIMATE AMENABILITY AND WEAKLY APPROXIMATE AMENABILITY OF THE SECOND DUALS OF BANACH ALGEBRAS

In this paper we study the approximately amenability and the weakly approximate amenability of second dual A** of the Banach algebra A. Indeed we show that the weakly approximate amenability of second dual A** implies the weakly approximate amenability of A if one of the following assertions holds (i) A is a left ideal in A** , (ii) A is a dual Banach algebra, (iii) A* is Arens regular and every derivation from A into A is weakly compact.