Skip to main content

Bands in partially ordered vector spaces with order unit

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)

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)
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: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Bas Lemmens
Date Deposited: 29 May 2014 10:40 UTC
Last Modified: 06 Feb 2020 04:09 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
  • Depositors only (login required):