فهرست نشریات علمی دسترسی آزاد ایران

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 $B$.