Reconstructing the Jordan structure of $C^{\ast }$-algebras from the metric on positive unit spheres

Chi-Wai Leung, Chi-Keung Ng, Ngai-Ching Wong

Let $A$ and $B$ be unital $C^{\ast }$-algebras, and let ${\mathrm{S}}_{A^{+}}$ and ${\mathrm{S}}_{B^{+}}$ denote their positive unit spheres. We first show that the diametral relation on the pos…