Document Type : Original Manuscript

Authors

Department of Mathematics, University of Birjand, P.O. Box 9717434765, Birjand, Iran.

10.22044/jas.2022.10734.1530

Abstract

In this paper, we introduce the concept of  module Lie  derivations on Banach algebras and study  module Lie  derivations on unital triangular Banach algebras $\mathcal{T}=\begin{bmatrix}A & M\\ &B\end{bmatrix}$ to its dual. Indeed, we prove that every module (linear) Lie derivation\linebreak $\delta: \mathcal{T} \to \mathcal{T}^{\ast}$  can be decomposed as $\delta = d + \tau$, where $d: \mathcal{T} \to \mathcal{T}^{\ast}$ is a module (linear) derivation and $\tau: \mathcal{T} \to Z_{\mathcal{T}}(\mathcal{T}^{\ast})$  is a module (linear) map vanishing at commutators if and only if this happens for the corner algebras $A$ and $B$.

Keywords

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