Geodesic
On the Linearity of Order-isomorphisms
Canadian journal of mathematics, Tome 73 (2021) no. 2, pp. 399-416

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DOI

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.
DOI : 10.4153/S0008414X1900066X
Mots-clés : order-isomorphism, affine map, inf-sup hull 
Lemmens, Bas; Gaans, Onno van; Imhoff, Hendrik van. On the Linearity of Order-isomorphisms. Canadian journal of mathematics, Tome 73 (2021) no. 2, pp. 399-416. doi: 10.4153/S0008414X1900066X
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     title = {On the {Linearity} of {Order-isomorphisms}},
     journal = {Canadian journal of mathematics},
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     year = {2021},
     volume = {73},
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     doi = {10.4153/S0008414X1900066X},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X1900066X/}
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