Some results on second transpose of a dual valued derivation

Let a be a banach algebra and x be an arbitrary banach a-module. in this paper, we study the second transpose of derivations with value in dual banach a-module x*. indeed, for a continuous derivation d : a → x* we obtain a necessary and sucient condition such that the bounded linear map ʌ o d'' : a**→ x*** to be a derivation, where ʌ is composition of restriction and canonical injection maps. this characterization generalizes some well known results in [2].