A geometric characterisation of real C*-algebras
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911803492007936 |
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| author | Chu, Cho-Ho |
| author_facet | Chu, Cho-Ho |
| contents | We characterise the positive cone of a real C*-algebra geometrically. Given an open cone $Ω$ in a real Banach space $V$, with closure $\overline Ω$, we show that $Ω$ is the interior of the positive cone of a unital real C*-algebra if and only if it is a Finsler symmetric cone with an orientable extension, which is equivalent to the condition that $V$ is, in an equivalent norm, the hermitian part of a unital real C*-algebra with positive cone $\overlineΩ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12628 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A geometric characterisation of real C*-algebras Chu, Cho-Ho Operator Algebras Functional Analysis 46L05 We characterise the positive cone of a real C*-algebra geometrically. Given an open cone $Ω$ in a real Banach space $V$, with closure $\overline Ω$, we show that $Ω$ is the interior of the positive cone of a unital real C*-algebra if and only if it is a Finsler symmetric cone with an orientable extension, which is equivalent to the condition that $V$ is, in an equivalent norm, the hermitian part of a unital real C*-algebra with positive cone $\overlineΩ$. |
| title | A geometric characterisation of real C*-algebras |
| topic | Operator Algebras Functional Analysis 46L05 |
| url | https://arxiv.org/abs/2403.12628 |