Weak and (-۱)-weak amenability of second dual of Banach algebras

For a Banach algebra A, A'' is (-۱)-Weakly amenable if A' is a Banach A''-bimodule and H^۱(A'',A')=\{۰\}. In this paper, among other things,  we study the relationships between the (-۱)-Weakly amenability of A'' and the weak amenability of A'' or A. Moreover, we show that the second dual of every C^\ast-algebra is (-۱)-Weakly amenable.

Keywords:

Banach algebra , point derivation , (-۱)-Weak amenability