An order-theoretic characterization of JB-algebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908906218848256 |
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| author | Roelands, Mark Tiersma, Samuel |
| author_facet | Roelands, Mark Tiersma, Samuel |
| contents | 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--Schäfer. These results have previously been established for finite-dimensional resp. reflexive order unit spaces by Walsh and Lemmens--R.--Wortel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An order-theoretic characterization of JB-algebras Roelands, Mark Tiersma, Samuel Functional Analysis 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--Schäfer. These results have previously been established for finite-dimensional resp. reflexive order unit spaces by Walsh and Lemmens--R.--Wortel. |
| title | An order-theoretic characterization of JB-algebras |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2507.09526 |