Abstract
Two axiomatic approaches to quantum mechanics are compared : the quantum-logic approach and the transition-probabi1ity spaces approach. It is shown that the quantum-logic approach is more general than the transition-probability spaces approach. Necessary and sufficient conditions -for the equivalence of these approaches are found. As a generalization of the above approaches, a notion of an orthogonality space is introduced. Conditions under which an orthogonality space can be represented in a generalized Hilbert space are investigated.
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© 1989 Kluwer Academic Publishers
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Pulmannova, S. (1989). Representations of Quantum Logics and Transition Probability Spaces. In: Bitsakis, E.I., Nicolaides, C.A. (eds) The Concept of Probability. Fundamental Theories of Physics, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1175-8_7
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DOI: https://doi.org/10.1007/978-94-009-1175-8_7
Publisher Name: Springer, Dordrecht
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