Numerical index one characterises commutative JB*-triples

Lei Li, Siyu Liu, Antonio M. Peralta

We establish that a JB${}^{\ast }$-triple $E$ is commutative if and only if its numerical index $n(E)$ is one. As a consequence, $n(E)=1$ implies $n(E^{\ast })=n(E^{\ast \ast })=1$. This settles a…