The inverse of band preserving and disjointness preserving operators
type: Item
instance of: scholarly article
title: The inverse of band preserving and disjointness preserving operators
zbMATH Open document ID: 0787.47031
DOI: 10.1016/0019-3577(92)90006-7
author: S. Singh
published in: Indagationes Mathematicae. New Series
publication date: 1992-12-15T00:00:00Z
review text: The question whether a bijective and band preserving operator \(T\) mapping an Archimedean vector lattice \(\mathcal E\) into \(\mathcal E\) has a band preserving inverse \(T^{-1}\) is answered in positive and generalized for two cases: (i) \(\mathcal E\) has the principal projection property; (ii) \(\mathcal E\) is relatively uniformly complete.
Mathematics Subject Classification ID: 47B65
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 78088
zbMATH Keywords: positive operator
zbMATH Keywords: Riesz homomorphism
zbMATH Keywords: bijective and band preserving operator
zbMATH Keywords: Archimedean vector lattice
zbMATH Keywords: band preserving inverse
zbMATH Keywords: principal projection property
zbMATH Keywords: relatively uniformly complete
reviewed by: Ivo Marek
MaRDI profile type: Publication
full work available at URL: 0019-3577(92)90006-7
OpenAlex ID: W2083979422
cites work: Q3308615
cites work: Q3889571
cites work: Q3949571
cites work: Lateral and Dedekind Completion of Archimedean Lattice Groups
cites work: Orthomorphisms of archimedean vector lattices
cites work: Q3135842
cites work: Q3868292
cites work: The order boundedness of band preserving operators on uniformly complete vector lattices
cites work: Q4100960
cites work: Banach lattices
cites work: A Note on Disjointness Preserving Operators
cites work: Order completeness and disjoint completeness of linear partially ordered spaces
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description: scientific article; zbMATH DE number 78088