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On the linearity of order-isomorphisms

Lemmens, Bas, Van Imhoff, Hent, van Gaans, Onno (2020) On the linearity of order-isomorphisms. Canadian journal of mathematics, . Article Number UNSPECIFIED. ISSN 1496-4279. E-ISSN 1496-4279. (doi:10.4153/S0008414X1900066X) (KAR id:73505)

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https://doi.org/10.4153/S0008414X1900066X

Abstract

A basic problem in the theory of partially ordered vector spaces is to characterise those cones on which every order-isomorphism is linear. We show that this is the case for every Archimedean cone that equals the inf-sup hull of the sum of its engaged extreme rays. This condition is milder than existing ones and is satisfied by, for example, the cone of positive operators in the space of bounded self-adjoint operators on a Hilbert space. We also give a general form of order-isomorphisms on the inf-sup hull of the sum of all extreme rays of the cone, which extends results of Artstein-Avidan and Slomka to infinite dimensional partially ordered vector spaces, and prove the linearity of homogeneous order-isomorphisms in a variety of new settings.

Item Type: Article
DOI/Identification number: 10.4153/S0008414X1900066X
Uncontrolled keywords: order-isomorphisms, affine maps, inf-sup hull
Subjects: 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: 16 Apr 2019 05:57 UTC
Last Modified: 07 Apr 2020 08:43 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/73505 (The current URI for this page, for reference purposes)
Lemmens, Bas: https://orcid.org/0000-0001-6713-7683
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