Abstract
The problem on geometric characterization of state spaces of operator algebras isimportant in the theory of such algebras. In the mid-80’s, Friedman and Russo introduced faciallysymmetric spaces for geometric characterization of the predual spaces of JBW \({}^\ast\) -triples that admit an algebraic structure. Manyproperties that are required in such characterizations are natural assumptions on state spaces ofphysical systems. These spaces are regarded as a geometric model for states in quantummechanics. In the present article, we prove that, for all reflexive atomic neutral strongly faciallysymmetric spaces \(X\) and \(Y\) , if a transform \(P:{{M}_{X}}\to {{M}_{Y}}\) preserves both orthogonality between geometrictriponents and the transition pseudo-probabilities then \(P\) can be extended to an isometric isomorphism from \({X}^{*}\) to \({Y}^{*}\) .
