Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682210220191213Some results on second transpose of a dual valued derivation267273419510.22075/ijnaa.2019.4195ENMorteza EssmailiDepartment of Mathematics, Faculty of Mathematical and Computer Science, Kharazmi University, 50 Taleghani Avenue, 15618 Tehran, IranJournal Article20180604Let $A$ 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