C*-algebras and Mackey's axioms |
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Authors: | Roger J. Plymen |
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Affiliation: | (1) Mathematical Institute, University of Oxford, UK;(2) Present address: Department of Mathematics, The University, Manchester 13, Great Britain |
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Abstract: | A non-commutative version of probability theory is outlined, based on the concept of a*-algebra of operators (sequentially weakly closedC*-algebra of operators). Using the theory of*-algebras, we relate theC*-algebra approach to quantum mechanics as developed byKadison with the probabilistic approach to quantum mechanics as axiomatized byMackey. The*-algebra approach to quantum mechanics includes the case of classical statistical mechanics; this important case is excluded by theW*-algebra approach. By considering the*-algebra, rather than the von Neumann algebra, generated by the givenC*-algebraA in its reduced atomic representation, we show that a difficulty encountered byGuenin concerning the domain of a state can be resolved. |
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