Riesz completions, functional representations and anti-lattices

Lemmens, Bas and Van Gaans, Onno and Kalauch, Anke (2013) Riesz completions, functional representations and anti-lattices. Positivity . ISSN 1385-1292. (In press) (The full text of this publication is not available from this repository)

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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
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Divisions: Central Services > Templeman Library
Central Services > Computing Service
Central Services > Management Information Systems
Central Services > Research Services
Depositing User: Bas Lemmens
Date Deposited: 04 Oct 2012 10:43
Last Modified: 23 Jan 2013 12:24
Resource URI: http://kar.kent.ac.uk/id/eprint/31248 (The current URI for this page, for reference purposes)
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