Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 10 2 2019 12 13 Some results on second transpose of a dual valued derivation 267 273 4195 10.22075/ijnaa.2019.4195 EN Morteza Essmaili Department of Mathematics, Faculty of Mathematical and Computer Science, Kharazmi University, 50 Taleghani Avenue, 15618 Tehran, Iran Journal Article 2018 06 04 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 [2]. https://ijnaa.semnan.ac.ir/article_4195_d36bb72cb9e9acb7cd765a8cfcd281bc.pdf