Automorphisms of Order Structures of Abelian Parts of Operator Algebras and Their Role in Quantum Theory

Abstract

© 2013, Springer Science+Business Media New York. It is shown that any order isomorphism between the structures of unital associative JB subalgebras of JB algebras is given naturally by a partially linear Jordan isomorphism. The same holds for nonunital subalgebras and order isomorphisms preserving the unital subalgebra. Finally, we recover usual action of time evolution group on a von Neumann factor from group of automorphisms of the structure of Abelian subalgebras.