Can one identify two unital JB${}^{\ast }$-algebras by the metric spaces determined by their sets of unitaries?

María Cueto-Avellaneda, Antonio M. Peralta

Let $M$ and $N$ be two unital JB${}^{\ast }$-algebras and let $\mathcal{U}(M)$ and $\mathcal{U}(N)$ denote the sets of all unitaries in $M$ and $N$, respectively. We prove that the follo…