Lemmens, Bas,
Kalauch, Anke,
van Gaans, Onno
(2015)
*
Bands in partially ordered vector spaces with order unit.
*
Positivity,
9
(3).
pp. 489-511.
ISSN 1385-1292.
(doi:10.1007/s11117-014-0311-7)
(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:41204)

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Official URL http://link.springer.com/article/10.1007%2Fs11117-... |

## Abstract

In an Archimedean directed partially ordered vector space X one can define the concept of a band in terms of disjointness. Bands can be studied by using a vector lattice cover Y of X. If X has an order unit, Y can be represented as C(?), where ? is a compact Hausdorff space. We characterize bands in X, and their disjoint complements, in terms of subsets of ?. We also analyze two methods to extend bands in X to C(?) and show how the carriers of a band and its extensions are related.

We use the results to show that in each n-dimensional partially ordered vector space with a closed generating cone, the number of bands is bounded by (1/4)2^(2^n) for n?2. We also construct examples of (n+1)-dimensional partially ordered vector spaces with (2n \choose n)+2 bands. This shows that there are n-dimensional partially ordered vector spaces that have more bands than an n-dimensional Archimedean vector lattice when n?4.

Item Type: | Article |
---|---|

DOI/Identification number: | 10.1007/s11117-014-0311-7 |

Subjects: |
Q Science 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: | 29 May 2014 10:40 UTC |

Last Modified: | 16 Feb 2021 12:53 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/41204 (The current URI for this page, for reference purposes) |

Lemmens, Bas: | https://orcid.org/0000-0001-6713-7683 |

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