Weak majorization and doubly substochastic operators on \(\ell^p(I)\)
type: Item
instance of: scholarly article
title: Weak majorization and doubly substochastic operators on \(\ell^p(I)\)
zbMATH Open document ID: 1353.47074
published in: Linear Algebra and its Applications
publication date: 2015-09-28T00:00:00Z
review text: Let \({\ell}^p(I)^+\) denote a set of all positive elements of the Banach space \({\ell}^p(I)\) with \(p\geq 1\), that is, \[ {\ell}^p(I)^+:=\{f\in{\ell}^p(I):f(i)\geq 0,\forall i\in I\}. \] Using the notion of a doubly substochastic operator, the author defines a weak majorization on \({\ell}^p(I)^+\) as follows. For \(f,g\in {\ell}^p(I)^+\), we say that \(f\) is weakly majorized by \(g\) if there exists a doubly substochastic operator \(D\) on \({\ell}^p(I)\) such that \(f=Dg\). Several properties of double substochastic operators and their relationship with the weak majorization are proved. In particular, it is shown that \(f\) is weakly majorized by \(g\) and \(g\) is weakly majorized by \(f\) if and only if there exists a partial permutation \(P\) such that \(g=Pf\).
Mathematics Subject Classification ID: 47B60
Mathematics Subject Classification ID: 15B51
zbMATH DE Number: 6485763
zbMATH Keywords: weak majorization
zbMATH Keywords: row, column and doubly substochastic operators
zbMATH Keywords: partial permutation
author: Martin Ljubenović
reviewed by: Mirosława Zima
MaRDI profile type: Publication
full work available at URL: j.laa.2015.08.020
OpenAlex ID: W1259866067
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DOI: 10.1016/J.LAA.2015.08.020
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description: scientific article; zbMATH DE number 6485763