All-derivable points in the algebra of all upper triangular matrices
type: Item
instance of: scholarly article
title: All-derivable points in the algebra of all upper triangular matrices
zbMATH Open document ID: 1145.47058
author: J. Zhu
author: Changping Xiong
author: Renyuan Zhang
published in: Linear Algebra and its Applications
publication date: 2008-07-10T00:00:00Z
review text: Let \(\mathcal{TM}_n\) be the algebra of all \(n\times n\) upper triangular matrices, and let \(L(\mathcal{TM}_n)\) denote the set of all linear mappings on \(\mathcal{TM}_n\). For \(\varphi\in L(\mathcal{TM}_n)\), \(\varphi\) is said to be a derivation if \(\varphi(ST)=\varphi(S)T+S\varphi(T)\) for any \(S,T\in\mathcal{TM}_n\). Fix a matrix \(G\in\mathcal{TM}_n\), then \(\varphi\in L(\mathcal{TM}_n)\) is said to be a derivable mapping at \(G\) if \(\varphi(ST)=\varphi(S)T+S\varphi(T)\) for any \(S,T\in\mathcal{TM}_n\) with \(ST=G\). In this paper, the authors prove that \(G\in\mathcal{TM}_n\) is an all derivable point of \(\mathcal{TM}_n\) if and only if \(G\neq0\).
Mathematics Subject Classification ID: 47L35
Mathematics Subject Classification ID: 47B47
zbMATH DE Number: 5299352
zbMATH Keywords: all derivable point
zbMATH Keywords: nest algebra
zbMATH Keywords: derivable linear mapping
reviewed by: Dachun Yang
MaRDI profile type: Publication
full work available at URL: j.laa.2008.04.010
OpenAlex ID: W1983074086
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DOI: 10.1016/J.LAA.2008.04.010
description: scientific article; zbMATH DE number 5299352