Nonlinear isometries on Schatten-\(p\) class in atomic nest algebras
type: Item
instance of: scholarly article
title: Nonlinear isometries on Schatten-\(p\) class in atomic nest algebras
zbMATH Open document ID: 1473.47052
DOI: 10.1155/2014/810862
author: Kan He
author: Qing Yuan
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Let \(H\) be a complex Hilbert space; denote by \(\operatorname{Alg} \mathcal N\) and \(\mathcal C_p(H)\) the atomic nest algebra associated with the atomic nest \(\mathcal N\) on \(H\) and the space of Schatten-\(p\) class operators on, \(H\) respectively. Let \(\mathcal C_p(H)\cap\operatorname{Alg} \mathcal N\) be the space of Schatten-\(p\) class operators in \(\operatorname{Alg} \mathcal N\). When \(1\leq p<+\infty\) and \(p\neq2\), we give a complete characterization of nonlinear surjective isometries on \(\mathcal C_p(H)\cap\operatorname{Alg} \mathcal N\). If \(p=2\), we also prove that a nonlinear surjective isometry on \(\mathcal C_2(H)\cap\operatorname{Alg} \mathcal N\) is the translation of an orthogonality preserving map.
Mathematics Subject Classification ID: 47L35
Mathematics Subject Classification ID: 47L20
Mathematics Subject Classification ID: 47H30
zbMATH DE Number: 7023124
zbMATH Keywords: complex Hilbert space
zbMATH Keywords: atomic nest algebra
zbMATH Keywords: Schatten-\(p\) class operators
zbMATH Keywords: nonlinear surjective isometries
zbMATH Keywords: orthogonality preserving map
Wikidata QID: Q59041715
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/810862
OpenAlex ID: W2010214419
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description: scientific article; zbMATH DE number 7023124