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Logics with given centers and state spaces


Author: Pavel Pták
Journal: Proc. Amer. Math. Soc. 88 (1983), 106-109
MSC: Primary 06C15; Secondary 03G12, 81B10
DOI: https://doi.org/10.1090/S0002-9939-1983-0691287-9
MathSciNet review: 691287
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Abstract: Let $ B$ be a Boolean algebra and let $ K$ be a compact convex subset of a locally convex topological linear space. Then there exists a logic with the center Boolean isomorphic to $ B$ and with the state space affinely homeomorphic to $ K$.


References [Enhancements On Off] (What's this?)

  • [1] J. Brabec and P. Pták, On compatibility in quantum logics, Found. Phys. 12 (1982), 207-212. MR 659779 (84h:81009)
  • [2] R. Greechie, Orthomodular lattices admitting no states, J. Combin. Theory Ser. A 10 (1971), 119-132. MR 0274355 (43:120)
  • [3] S. Gudder, Uniqueness and existence properties of bounded observables, Pacific J. Math. 19 (1966), 81-93. MR 0201146 (34:1030)
  • [4] -, Stochastic methods in quantum mechanics, Elsevier, North-Holland, Amsterdam, 1979. MR 543489 (84j:81003)
  • [5] V. Maňasová and P. Pták, On states on the product of logics, Internat. J. Theoret. Phys. 20 (1981), 451-456. MR 632598 (82j:81008)
  • [6] F. W. Shultz, A characterization of state spaces of orthomodular lattices, J. Combin. Theory Ser. A 17 (1974), 317-328. MR 0364042 (51:297)
  • [7] V. Varadarajan, Geometry of quantum theory, vol. 1, Van Nostrand Reinhold, Princeton, N. J., 1968. MR 0471674 (57:11399)

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DOI: https://doi.org/10.1090/S0002-9939-1983-0691287-9
Article copyright: © Copyright 1983 American Mathematical Society

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