On automatic continuity of the derivations on module extension of Banach algebras

TL;DR

This paper investigates the structure and automatic continuity of derivations on module extensions of Banach algebras, providing insights into their behavior and properties.

Contribution

It characterizes the structure of derivations on module extensions and establishes conditions for their automatic continuity.

Findings

Derived structural descriptions of derivations on module extensions.

Proved automatic continuity results for these derivations.

Enhanced understanding of derivations in the context of Banach algebra modules.

Abstract

In this article we shall focus on the derivations on module extension of Banach algebras and determine the general structure of them. Then we obtain some results concerning the automatic continuity of these mappings.