Extending monotone seminorms on partially ordered vector spaces
type: Item
instance of: scholarly article
title: Extending monotone seminorms on partially ordered vector spaces
zbMATH Open document ID: 0946.46004
DOI: 10.1016/S0019-3577(98)80003-7
author: O. W. van Gaans
published in: Indagationes Mathematicae. New Series
publication date: 1999-02-17T00:00:00Z
review text: Let \(E\) be a partially ordered vector space, \(E_0\) be a majorizing subspace of \(E\), and \(p\) be a monotone seminorm on \(E_0\), that is, \(p(u)\leq p(v)\) provided \(u,v\in E^+_0\) and \(u\leq v\). The author finds a necessary and sufficient condition under which \(p\) admits a monotone extension to \(E\). The uniqueness of this extension and its completeness are discussed. There are also several interesting examples illustrating the results obtained.
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 46A22
zbMATH DE Number: 1251196
zbMATH Keywords: partially ordered vector space
zbMATH Keywords: majorizing subspace
zbMATH Keywords: monotone seminorm
zbMATH Keywords: monotone extension
reviewed by: Y. A. Abramovich
MaRDI profile type: Publication
cites work: Q3139959
cites work: Tensor products of Banach lattices
cites work: Q5555984
cites work: Q5613420
full work available at URL: s0019-3577(98)80003-7
OpenAlex ID: W2053769623
description: scientific article; zbMATH DE number 1251196