Lemmens, Bas, Van Imhoff, Hent, van Gaans, Onno (2021) On the linearity of order-isomorphisms. Canadian journal of mathematics, 73 (2). pp. 399-416. ISSN 1496-4279. E-ISSN 1496-4279. (doi:10.4153/S0008414X1900066X) (KAR id:73505)
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Official URL: 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 |
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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: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | Bas Lemmens |
Date Deposited: | 16 Apr 2019 05:57 UTC |
Last Modified: | 09 Dec 2022 00:04 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/73505 (The current URI for this page, for reference purposes) |
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