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Riesz completions, functional representations and anti-lattices

Lemmens, Bas, van Gaans, Onno, Kalauch, Anke (2014) Riesz completions, functional representations and anti-lattices. Positivity, 18 (1). pp. 201-218. ISSN 1385-1292. (doi:DOI 10.1007/s11117-013-0240-x) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:31248)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
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http://www.springerlink.com/content/102984/

Abstract

We show that the Riesz completion of an Archimedean partially or- dered vector space X with unit can be represented as a norm dense Riesz subspace of the smallest functional representation of X. This yields a con- venient way to compute the Riesz completion. To illustrate the method, the Riesz completions of spaces ordered by Lorentz cones, cones of sym- metric positive semi-definite matrices, and polyhedral cones are deter- mined. We use the representation to investigate the existence of non- trivial disjoint elements and link the absence of such elements to the no- tion of anti-lattice. One of the results is a geometric condition on the dual cone of a finite dimensional partially ordered vector space X that ensures that X is an anti-lattice.

Item Type: Article
DOI/Identification number: DOI 10.1007/s11117-013-0240-x
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Bas Lemmens
Date Deposited: 04 Oct 2012 10:43 UTC
Last Modified: 06 Feb 2020 04:07 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/31248 (The current URI for this page, for reference purposes)
Lemmens, Bas: https://orcid.org/0000-0001-6713-7683
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