Maps preserving Schatten \(p\)-norms of convex combinations
type: Item
instance of: scholarly article
title: Maps preserving Schatten \(p\)-norms of convex combinations
zbMATH Open document ID: 1473.47014
DOI: 10.1155/2014/520795
author: Xianqiang Yang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We study maps \(\phi\) of positive operators of the Schatten \(p\)-classes (\(1 < p < + \infty\)), which preserve the \(p\)-norms of convex combinations, that is, \(\| t \rho +(1 - t) \sigma \|_p = \| t \phi(\rho) +(1 - t) \phi(\sigma) \parallel_p\), \(\forall \rho, \sigma \in \mathcal{S}_p^+(H)_1\), \(t \in [0,1]\). They are exactly those carrying the form \(\phi(\rho) = U \rho U^*\) for a unitary or antiunitary \(U\). In the case \(p = 2\), we have the same conclusion whenever it just holds \(\| \rho + \sigma \|_2 = \| \phi(\rho) + \phi(\sigma) \|_2\) for all the positive Hilbert-Schmidt class operators \(\rho, \sigma\) of norm 1. Some examples are demonstrated.
Mathematics Subject Classification ID: 47B49
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 7022546
zbMATH Keywords: maps preserving Schatten \(p\)-norms
zbMATH Keywords: positive Hilbert-Schmidt class operators
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/520795
OpenAlex ID: W2083630024
Wikidata QID: Q59039107
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description: scientific article; zbMATH DE number 7022546