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arXiv · 2507.09526

An order-theoretic characterization of JB-algebras

Mark Roelands·Samuel Tiersma
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Abstract

We give an order-theoretic characterization of the JB-algebras among the complete order unit spaces in terms of the existence of an order-anti-automorphism of the interior of the cone that is homogeneous of degree -1. More geometrically, we characterize JB-algebras as those complete order unit spaces for which the interior of the cone is a symmetric Banach--Finsler manifold under Thompson's metric. Furthermore, we show that two order unit spaces are isomorphic if there exists a gauge-reversing bijection between them, thus answering a question raised by Noll--Sch\"afer. These results have previously been established for finite-dimensional resp. reflexive order unit spaces by Walsh and Lemmens--R.--Wortel.

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Mark Roelands, Samuel Tiersma. 2025-07-13. An order-theoretic characterization of JB-algebras. https://arxiv.org/abs/2507.09526

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