On spaces in which the norm convergence coincides with the order convergence

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 1973 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 13, pages 158-163 (issn: 0001-4346, eissn: 1573-8876,

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Authors: Vulikh, B. Z.; Korsakova, O. S.;

doi: 10.1007/bf01094235

On spaces in which the norm convergence coincides with the order convergence

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Abstract

We investigate partially ordered normed vector spaces in which the norm convergence coincides with the order convergence. We consider spaces where the convergences coincide for arbitrary nets and spaces where the convergences coincide only for sequences. We give conditions which characterize such spaces and investigate their properties. In particular, we study the problem of their Dedekind completeness and σ-completeness.

Related Organizations

St Petersburg University
Russian Federation
Gorno-Altaisk State University
Russian Federation

Keywords

Isomorphic theory (including renorming) of Banach spaces, Ordered topological linear spaces, vector lattices

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