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A note on the extensibility of states. (English) Zbl 0469.03044


MSC:

03G12 Quantum logic
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
06C15 Complemented lattices, orthocomplemented lattices and posets

Citations:

Zbl 0388.03025
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References:

[1] GUDDER S. P.: Uniqueness and existence properties of bounded observables. Pacific J. Math., 19, 1966, 81-93. · Zbl 0149.23603 · doi:10.2140/pjm.1966.19.81
[2] RÜTTIMANN G. T.: Jauch-Piron states. J. Math. Phys., 18, 1977, 189-193. · Zbl 0388.03025 · doi:10.1063/1.523255
[3] VARADARAJAN V. S.: Probability in physics and a theorem of simultaneous observability. Commun. Pure Appl. Math., 15, 1962, 189-217. · Zbl 0109.44705 · doi:10.1002/cpa.3160150207
[4] VARADARAJAN V. S.: Geometry of Quantum Theory. Vol. 1, van Nostrand, Princeton 1968. · Zbl 0155.56802
[5] GUDDER S. P.: System of observables in axiomatic quantum mechanics. J. Math. Phys., 8, 1967, 2109-2113. · Zbl 0161.23404 · doi:10.1063/1.1705127
[6] GUDDER S. P.: Spectral methods for a generalized probability theory. Trans. Amer. Math. Soc., 119, 1965, 428-442. · Zbl 0161.46105 · doi:10.2307/1994077
[7] GLEASON A. M.: Measures on the closed subspaces of a Hilbert space. J. Rat. Mech. Anal., 6, 1957, 885-894. · Zbl 0078.28803
[8] DIXMIER J.: Les algebres d’opérateurs dans ľespace Hilbertien. Gauthier-villars, Paris 1969.
[9] BADE W. G.: On Boolean algebras of projections and algebras of operators. Trans. Amer. Math. Soc., 80, 1955, 345-360. · Zbl 0066.36202 · doi:10.2307/1992993
[10] DUNFORD N., SCHWARTZ J. T.: Линєйныє опєраторы. Спєктральныє опєраторы. МИР, Москва 1974.
[11] ZIERLER N.: Axioms for non-relativistic quantum mechanics. Pacific J. Math., 11, 1961, 1151-1169. · Zbl 0138.44503 · doi:10.2140/pjm.1961.11.1151
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