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Measures on projections and physical states. (English) Zbl 0507.46052


MSC:

46L51 Noncommutative measure and integration
46L53 Noncommutative probability and statistics
46L54 Free probability and free operator algebras
46L10 General theory of von Neumann algebras
46L30 States of selfadjoint operator algebras
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
46C99 Inner product spaces and their generalizations, Hilbert spaces
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References:

[1] Aarnes, J.F.: Quasi-states onC*-algebras. Trans. Am. Math. Soc.149, 601-625 (1970) · Zbl 0212.15403
[2] Dixmier, J.: LesC*-algebres et leurs representations. Paris: Gauthier-Villars 1969
[3] Gleason, A.M.: Measures on closed subspaces of a Hilbert space. J. Math. Mech.6, 885-893 (1957) · Zbl 0078.28803
[4] Gunson, J.: Physical states on quantum logics. I. Ann. Inst. Henri Poincar? A17, 295-311 (1972)
[5] Jauch, J.M.: Foundations of quantum mechanics. Reading. Mass.: Addison-Wesley 1968 · Zbl 0166.23301
[6] Mackey, G.W.: Quantum mechanics and Hilbert space. Am. Math. Month.64, 45-57 (1957) · Zbl 0137.23805 · doi:10.2307/2308516
[7] Pedersen, G.K.:C*-algebras and their automorphism groups. New York: Academic Press 1979 · Zbl 0416.46043
[8] Takesaki, M.: Theory of operator algebras. I. Berlin, Heidelberg, New York: Springer 1979 · Zbl 0436.46043
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