Some results on second transpose of a dual valued derivation

Document Type : Research Paper


Department of Mathematics, Faculty of Mathematical and Computer Science, Kharazmi University, 50 Taleghani Avenue, 15618 Tehran, Iran


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 $D:A\longrightarrow X^{*}$ we obtain a necessary and sufficient condition such that the bounded linear map $\Lambda\circ D^{\prime\prime}:A^{**}\longrightarrow X^{***}$ to be a derivation, where $\Lambda$ is composition of restriction and canonical injection maps. This characterization generalizes some well known results in \cite{aef}.