Document Type : Research Paper

Author

• Morteza Essmaili

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

Abstract

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 $X^{\ast }.$ Indeed, for a continuous derivation $D:A⟶X^{\ast }$ we obtain a necessary and sufficient condition such that the bounded linear map $\mathrm{\Lambda }\circ D^{\prime \prime }:A^{\ast \ast }⟶X^{\ast \ast \ast }$ to be a derivation, where $\mathrm{\Lambda }$ is composition of restriction and canonical injection maps. This characterization generalizes some well known results in [2].

Keywords

• Derivation
• second transpose
• Banach module
• module actions