# 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)

## 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 10.1007/s11117-014-0311-7 Q ScienceQ Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Bas Lemmens 29 May 2014 10:40 UTC 16 Feb 2021 12:53 UTC https://kar.kent.ac.uk/id/eprint/41204 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-6713-7683