C. Ng

Reconstructing the Jordan structure of $C^*$-algebras from the metric on positive unit spheres

Let $A$ and $B$ be unital $C^*$-algebras, and let $\mathrm{S}_{A^+}$ and $\mathrm{S}_{B^+}$ denote their positive unit spheres. We first show that the diametral relation on the positive unit sphere already determines Jordan structure. More precisely, suppose that $\Lambda:\mathrm{S}_{A^+}\to\mathrm{S}_{B^+}$ is a bijec...