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. | |

Official URL: 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: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |

Depositing User: | Bas Lemmens |

Date Deposited: | 04 Oct 2012 10:43 UTC |

Last Modified: | 17 Aug 2022 10:56 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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