Abstract
We characterise the positive cone of a real C*-algebra geometrically. Given an open cone Ω in a real Banach space V, with the closure \(\overline \Omega \), 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 the positive cone \(\overline \Omega \).
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This work was supported by the Engineering and Physical Sciences Research Council, UK (Grant No. EP/R044228/1).
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Chu, CH. A geometric characterisation of real C*-algebras. Sci. China Math. 66, 2277–2292 (2023). https://doi.org/10.1007/s11425-022-2041-8
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DOI: https://doi.org/10.1007/s11425-022-2041-8