Determinacy of Functionals and Lyapunov Theorem for Jordan Triple Structures and von Neumann Algebras

Abstract

In this note we apply noncommutative versions of Lyapunov convexity theorem to obtaning new results in comparison theory of states and functional on von Neumann algebras and $$JBW^{\ast}$$ triples. We show that in many cases the sets of projections or tripotents on which functionals attain constant single numerical value are determining for them. We discuss connection of our results with quantum theory.