A note on weak orthomorphisms
type: Item
instance of: scholarly article
title: A note on weak orthomorphisms
zbMATH Open document ID: 1177.06023
author: Elmiloud Chil
published in: Archiv der Mathematik
publication date: 2009-06-16T00:00:00Z
review text: Let \(E\) be a relatively uniformly complete vector lattice, \(D\) a vector sublattice. An order-bounded linear operator \(T: D\to E\) is called an orthomorphism if \(|x|\wedge|y|= 0\) in \(D\) implies \(|T(x)|\wedge|y|= 0\) in \(E\). It is weak if \(D\) is order-dense in \(E\). A weak orthomorphism is called extended orthomorphism if \(D\) is an order ideal in \(E\). The author proves that weak orthomorphism and extended orthomorphism coincide.
reviewed by: Beloslav Riečan
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 47B65
zbMATH DE Number: 5565242
zbMATH Keywords: extended orthomorphism
zbMATH Keywords: weak orthomorphism
zbMATH Keywords: vector lattice
MaRDI profile type: Publication
full work available at URL: s00013-009-2923-x
OpenAlex ID: W2013932268
DOI: 10.1007/S00013-009-2923-X
description: scientific article; zbMATH DE number 5565242