A relationship between the space of orthomorphisms and the centre of a vector lattice
type: Item
instance of: scholarly article
title: A relationship between the space of orthomorphisms and the centre of a vector lattice
zbMATH Open document ID: 1334.46002
author: Elmiloud Chil
author: Bourokba Hassen
author: Mokaddem Mohamed
published in: Positivity
publication date: 2015-09-22T00:00:00Z
review text: The authors consider an arbitrary vector lattice \(\mathbb{Z}\). Recall that the centre \(\mathbb{Z}(E)\) of \(E\) consists of all linear operators on \(E\) which are bounded by some multiple of the identity. Consider the collection \(\mathrm{Orth}(E)\) of all orthomorphisms on \(E\). The authors show that \(\mathbb{Z}(\mathrm{Orth\,} E)\) and \(\mathbb{Z}(E)\) are isomorphic, and then they give a necessary and sufficient condition for the equality \(\mathrm{Orth}(E)= \mathbb{Z}(E)\). It is given in terms of Banach lattices.
reviewed by: Beloslav Riečan
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 06F20
zbMATH DE Number: 6484278
zbMATH Keywords: orthomorphisms
zbMATH Keywords: ideal centre
zbMATH Keywords: vector lattice
MaRDI profile type: Publication
full work available at URL: s11117-014-0308-2
OpenAlex ID: W2072996726
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DOI: 10.1007/S11117-014-0308-2
description: scientific article; zbMATH DE number 6484278