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arXiv · 2609.07710

Numerical index one characterises commutative JB*-triples

Lei Li·Siyu Liu·Antonio M. Peralta
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Abstract

We establish that a JB$^*$-triple $E$ is commutative if and only if its numerical index $n(E)$ is one. As a consequence, $n(E) = 1$ implies $n(E^*) = n(E^{**}) = 1$. This settles a question left open in the literature since 2008.

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Lei Li, Siyu Liu, Antonio M. Peralta. 2026-09-07. Numerical index one characterises commutative JB*-triples. https://arxiv.org/abs/2609.07710

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