Automorphisms of Order Structures of Abelian Parts of Operator Algebras and Their Role in Quantum Theory |
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| Authors: | Jan Hamhalter Ekaterina Turilova |
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| Institution: | 1. Faculty of Electrical Engineering, Department of Mathematics, Czech Technical University, Technicka 2, 166 27, Prague 6, Czech Republic
2. Institute of Computer Mathematics and Information Technologies, Kazan Federal University, Kremlevskaya 18, Kazan, Russia
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| Abstract: | 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. |
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