Diameters of state spaces of Jordan Banach algebras

The notion of diameter $D(A)$ of the state space of a Jordan Banach algebra ($JBW$-algebra $A$) is introduced. The diameters of the state spaces for $JBW$-factors of type $\mathrm I_n$ ($n<+\infty$), $\mathrm I_\infty$, $\mathrm{II}_1$, $\mathrm{II}_\infty$, $\mathrm{III}_\lambda$ ($0<\lambda<1$) are computed.
It is proved that if $A$ is not a factor, or is a factor of type $\mathrm I_\infty$ or $\mathrm{II}_1$, then $D(A)=2$. If $A$ is a $JBW$-factor of type $\mathrm I_n$ ($n<+\infty$), then $D(A)=2(1-1/n)$, and if $A$ is a $JBW$-factor of type $\mathrm{III}_\lambda$ ($0<\lambda<1$), then $D(A)=2(1-\sqrt\lambda)/(1+\sqrt\lambda)$ or $D(A)=2(1-\sqrt[4]\lambda)/(1+\sqrt[4]\lambda)$.
Bibliography: 15 titles.