A closed graph theorem for order bounded operators

dc.contributor.authorVan der Walt, Jan Harm
dc.contributor.emailjanharm.vanderwalt@up.ac.zaen_ZA
dc.date.accessioned2016-03-01T12:35:01Z
dc.date.issued2016
dc.description.abstractThe closed graph theorem is one of the cornerstones of linear functional analysis in Frechet spaces, and the extension of this result to more general topological vector spaces is a difficult problem comprising a great deal of technical difficulty. However, the theory of convergence vector spaces provides a natural framework for closed graph theorems. In this paper we use techniques from convergence vector space theory to prove a version of the closed graph theorem for order bounded operators on Archimedean vector lattices. This illustrates the usefulness of convergence spaces in dealing with problems in vector lattice theory, problems that may fail to be amenable to the usual Hausdorff-Kuratowski-Bourbaki concept of topology.en_ZA
dc.description.embargo2017-04-30
dc.description.librarianhb2015en_ZA
dc.description.urihttp://www.tandfonline.com/loi/tqma20en_ZA
dc.identifier.citationJan Harm van der Walt (2016) A closed graph theorem for order bounded operators, Quaestiones Mathematicae, 39:2, 167-178, DOI: 10.2989/16073606.2015.1068235.en_ZA
dc.identifier.issn0379-9468 (print)
dc.identifier.issn1727-933X (online)
dc.identifier.other10.2989/16073606.2015.1068235
dc.identifier.urihttp://hdl.handle.net/2263/51637
dc.language.isoenen_ZA
dc.publisherRoutledgeen_ZA
dc.rights© Taylor and Francis. This is an electronic version of an article published in Quaestiones Mathematicae, vol. 39, no. 2, pp. 167-178, 2016. doi : 10.2989/16073606.2015.1068235. Quaestiones Mathematicae is available online at : http://www.tandfonline.comloi/tqma20.en_ZA
dc.subjectVector latticeen_ZA
dc.subjectConvergence vector spaceen_ZA
dc.subjectOrder bounded operatoren_ZA
dc.titleA closed graph theorem for order bounded operatorsen_ZA
dc.typePostprint Articleen_ZA

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