Additive mappings that preserve rank one nilpotent operators.
type: Item
instance of: scholarly article
title: Additive mappings that preserve rank one nilpotent operators.
zbMATH Open document ID: 1046.47031
DOI: 10.1016/S0024-3795(02)00617-1
author: Wu Jing
author: Shijie Lu
author: Pengtong Li
published in: Linear Algebra and its Applications
publication date: 2003-05-27T00:00:00Z
review text: Let \(B(X)\) be the algebra of bounded operators on a complex infinite-dimensional Banach space \(X\) and \(F(X)\) be the subalgebra of all finite rank operators in \(B(X)\). A characterization of additive maps on \(F(X)\) which preserve rank one nilpotent operators in both directions is given. As application of this result, some additive preservers are obtained.
Mathematics Subject Classification ID: 47B49
Mathematics Subject Classification ID: 47L10
zbMATH DE Number: 1917813
zbMATH Keywords: additive preservers
zbMATH Keywords: nilpotents
zbMATH Keywords: potents
zbMATH Keywords: idempotents
zbMATH Keywords: rank
reviewed by: Jianlian Cui
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1917813