Additive idempotence preservers
type: Item
instance of: scholarly article
title: Additive idempotence preservers
zbMATH Open document ID: 1045.47033
DOI: 10.1016/S0024-3795(02)00340-3
published in: Linear Algebra and its Applications
publication date: 2003-02-05T00:00:00Z
review text: Let \(\mathcal A\) be a local matrix algebra over a field of characteristic different from 2, \(\mathcal B\) an arbitrary algebra, and \(X\), \(Y\) Banach spaces. Additive maps \(\Phi :{\mathcal A}\rightarrow \mathcal B\) which preserve idempotents are characterized. The result is then used in classifying additive surjections \(\Phi :{\mathcal B}(X)\rightarrow {\mathcal B}(Y)\) which preserve idempotents and do not annihilate finite-rank operators.
Mathematics Subject Classification ID: 47B49
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 1864736
zbMATH Keywords: additive preserver
zbMATH Keywords: idempotent
zbMATH Keywords: Jordan map
author: Bojan Kuzma
reviewed by: Jianlian Cui
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1864736