Linear rank and corank preserving maps on \({\mathcal B}(H)\) and an application to \(^*\)-semigroup isomorphisms of operator ideals
type: Item
instance of: scholarly article
title: Linear rank and corank preserving maps on \({\mathcal B}(H)\) and an application to \(^*\)-semigroup isomorphisms of operator ideals
zbMATH Open document ID: 0940.46012
DOI: 10.1016/S0024-3795(98)10045-9
author: Lajos Molnár
author: Peter Šemrl
author: Máté Győry
published in: Linear Algebra and its Applications
publication date: 2000-07-19T00:00:00Z
review text: The article presents some results in the sphere of linear operators in Hilbert space. Let \(B(H)\) be the algebra of all bounded linear operators on the Hilbert space \(H\). Let \(\phi\) be a linear map \(\phi:B(H)\to B(H)\) and \(\phi\) be preserving rank or corank, or nonincreasing rank of all elements of \(B(H)\). The structure of the map \(\phi\) is also shown in the work. Besides, the authors prove theorems on isomorphisms of operator ideals in \(B(H)\). For finite-dimensional results see \textit{L. B. Beasley} [Linear Algebra Appl. 107, 161-167 (1988; Zbl 0651.15004)] and \textit{R. Loewy} [Linear Multilinear Algebra 34, No. 1, 21-32 (1993; Zbl 0801.15002)], for infinite-dimensional results rank \(=1\) see \textit{J. Hou} [Sci. China, Ser. A 32, No. 8, 929-940 (1989; Zbl 0686.47030)] and \textit{M. Omladič} and \textit{P. Šemrl} [Linear Algebra Appl. 182, 239-256 (1993; Zbl 0803.47026)].
Mathematics Subject Classification ID: 46C07
Mathematics Subject Classification ID: 47B49
Mathematics Subject Classification ID: 47L20
zbMATH DE Number: 1370016
zbMATH Keywords: rank preserver
zbMATH Keywords: corank preserver
zbMATH Keywords: isomorphisms of operator ideals
reviewed by: Vladimir N. Karpushkin
MaRDI profile type: Publication
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full work available at URL: s0024-3795(98)10045-9
OpenAlex ID: W2074719135
description: scientific article; zbMATH DE number 1370016