THE STRUCTURE OF MODULE LIE DERIVATIONS ON TRIANGULAR BANACH ALGEBRAS | ||
| Journal of Algebraic Systems | ||
| دوره 11، شماره 1، آذر 2023، صفحه 15-26 اصل مقاله (134.62 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.10734.1530 | ||
| نویسندگان | ||
| Mohammad Reza Miri؛ Ebrahim Nasrabadi* ؛ Ali Reza Ghorchizadeh | ||
| Department of Mathematics, University of Birjand, P.O. Box 9717434765, Birjand, Iran. | ||
| چکیده | ||
| 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 $B$. | ||
| کلیدواژهها | ||
| triangular Banach algebra؛ module Lie derivation؛ standard Lie derivation | ||
| مراجع | ||
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