On the modulus of measures with values in topological Riesz spaces.
type: Item
instance of: scholarly article
title: On the modulus of measures with values in topological Riesz spaces.
zbMATH Open document ID: 1035.46031
author: Witold Wnuk
author: Lech Drewnowski
published in: Revista Matemática Complutense
publication date: 2002-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/44375
review text: Measures from an algebra into a topological Riesz space are studied with particular concern for the existence of the modulus for a given measure. The authors demonstrate, for example, a countably additive measure to the Banach lattice \textit{c} with no modulus, in fact, no absolute majorant. An extensive analysis of properties of the measure versus properties of the majorant is presented. These include extensions of known results; for example, conditions ensuring that the modulus of a countably additive measure is also countably additive. Interesting constructions are provided for spaces with a measure which is a countably additive with the property that the modulus exists but is not countably additive. Consequences for operators and the modulus of an operator are considered utilizing a condition related to weakly compact. To cite one example, it is established that for a Banach lattice \(E\) with appropriate properties, if an order bounded weakly compact operator from the space of bounded measurable functions to \(E\) has a modulus (exists properly), then \(| T| \) is also weakly compact.
reviewed by: William A. Feldman
Mathematics Subject Classification ID: 46G10
Mathematics Subject Classification ID: 46B42
zbMATH DE Number: 1908110
zbMATH Keywords: vector valued measure
zbMATH Keywords: topological Riesz space
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1908110