Uniform exhaustivity and Banach lattices
type: Item
instance of: scholarly article
title: Uniform exhaustivity and Banach lattices
zbMATH Open document ID: 0625.46028
DOI: 10.1007/BF01760811
author: Wayne C. Bell
author: Russell G. Bilyeu
author: Paul Lewis
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1986-01-01T00:00:00Z
review text: The measure theoretic notion of strong boundedness is extended to the setting of a real \(\sigma\)-complete Banach lattice X; the lattice theoretic concept which corresponds to strong boundedness is termed exhaustivity. Uniformly exhaustive subsets of X are studied, and various characterizations are presented. One of these characterizations involves the order continuity of the norm on X. The exhaustive elements of certain classical lattices are cataloged. Applications are given to spaces of measures.
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 46E27
zbMATH DE Number: 4015446
zbMATH Keywords: strong boundedness
zbMATH Keywords: \(\sigma \)-complete Banach lattice
zbMATH Keywords: exhaustivity
zbMATH Keywords: Uniformly exhaustive subsets
zbMATH Keywords: order continuity of the norm
zbMATH Keywords: spaces of measures
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01760811
OpenAlex ID: W2084336253
description: scientific article; zbMATH DE number 4015446