The uniform boundedness principle for order bounded operators
type: Item
instance of: scholarly article
title: The uniform boundedness principle for order bounded operators
zbMATH Open document ID: 0691.46003
DOI: 10.1155/S0161171289000621
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46443
review text: It is shown that for a sequence of order bounded linear operators from a Dedekind \(\sigma\)-complete vector lattice to a Dedekind complete vector lattice with an order unit which is order bounded pointwise is uniformly order bounded on order bounded subsets. By an example it is shown that the result does not hold if the vector lattices are assumed to be Dedekind complete, but there is no order unit in the image space.
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 4131007
zbMATH Keywords: sequence of order bounded linear operators from a Dedekind \(\sigma\)- complete vector lattice to a Dedekind complete vector lattice with an order unit
zbMATH Keywords: order bounded pointwise
zbMATH Keywords: uniformly order bounded on order bounded subsets
author: Charles Swartz
reviewed by: Tage Bai Andersen
MaRDI profile type: Publication
OpenAlex ID: W1974534944
description: scientific article; zbMATH DE number 4131007