Lw*wc AND Rw*wc AND WEAK AMENABILITY OF BANACH ALGEBRAS

We introduce some new concepts as left-weak*-weak convergence property [Lw*wc-property] and right-weak*-weak convergence property [Rw*wc-property] for Banach algebra A. Suppose that A and A**, respectively, have Rw*wc-property and Lw*wc-property, then if A** is weakly amenable, it follows that A is weakly amenable. Let D : A\to A** be a surjective derivation. If Dʹʹ is a derivation, then A is Arens regular.