\(d\)-independence and \(d\)-bases
type: Item
instance of: scholarly article
title: \(d\)-independence and \(d\)-bases
zbMATH Open document ID: 1046.46005
DOI: 10.1023/A:1025876218015
published in: Positivity
publication date: 2003-11-10T00:00:00Z
review text: In this note the authors formulate some questions concerning the notion of a \(d\)-basis which is a convenient tool for the investigation of properties of disjointness preserving operators. Some very basic and natural questions about \(d\)-bases remain open and this might be one of the major obstacles in obtaining a complete understanding of the structure of disjointness preserving operators between vector lattices. For example, in the first problem they ask: is it true that every maximal \(d\)-independent system in an arbitrary vector lattice \(X\) is a \(d\)-basis? If \(X\) is a vector lattice with a cofinal family of projection bands, the answer is affirmative.
reviewed by: Lahcène Mezrag
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 46B40
Mathematics Subject Classification ID: 46B42
zbMATH DE Number: 2002008
zbMATH Keywords: band
zbMATH Keywords: cofinal family
zbMATH Keywords: \(d\)-independent
zbMATH Keywords: \(d\)-basis
zbMATH Keywords: vector lattice
author: Y. A. Abramovich
author: Arkady Kitover
MaRDI profile type: Publication
full work available at URL: a:1025876218015
OpenAlex ID: W38404486
description: scientific article; zbMATH DE number 2002008