%0 Journal Article
%T Some results on second transpose of a dual valued derivation
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Essmaili, Morteza
%D 2019
%\ 12/13/2019
%V 10
%N 2
%P 267-273
%! Some results on second transpose of a dual valued derivation
%K Derivation
%K second transpose
%K Banach module
%K module actions
%R 10.22075/ijnaa.2019.4195
%X 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].
%U https://ijnaa.semnan.ac.ir/article_4195_d36bb72cb9e9acb7cd765a8cfcd281bc.pdf