Maharam extensions of positive operators and \(f\)-modules
type: Item
instance of: scholarly article
title: Maharam extensions of positive operators and \(f\)-modules
zbMATH Open document ID: 1061.47037
DOI: 10.1023/A:1015249114403
published in: Positivity
publication date: 2002-08-21T00:00:00Z
review text: Among other things, it is proved that, for suitable extensions of collections of positive order-continuous linear functionals on vector lattices, the assertion of the Radon-Nikodym theorem is true. The main result of the paper provides a way to construct a simultaneous extension of collections of positive linear operators between Archimedean Riesz spaces to Maharam (i.e., interval-preserving) operators between certain Dedekind complete Riesz spaces. The technique of construction of such extensions is based upon properties of the so-called \(f\)-modules.
Mathematics Subject Classification ID: 47B65
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 06F25
Mathematics Subject Classification ID: 47A20
zbMATH DE Number: 1785640
zbMATH Keywords: vector lattice
zbMATH Keywords: positive operator
zbMATH Keywords: Radon-Nikodym theorem
zbMATH Keywords: Maharam extension
author: W. A. J. Luxemburg
author: B. de Pagter
reviewed by: A. Rontó
MaRDI profile type: Publication
full work available at URL: a:1015249114403
OpenAlex ID: W192393231
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description: scientific article; zbMATH DE number 1785640