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Moment problem for effect algebras. (English) Zbl 0889.03056
The classical moment problem considers the question whether for a given sequence \(a_0,a_1,a_2,\ldots\) of non-negative reals there does exist a probability measure \(\mu\) on the Borel subsets of \([0,1]\) such that \(a_n=\int\limits_0^1t^nd\mu(t)\) for all non-negative integers \(n\). A generalized version of this problem is investigated in effect algebras and also for so-called generalized observables. Some solutions are presented. The relation to a certain property, the so-called E-property, is established.
Reviewer: H.Länger (Wien)

MSC:
03G12 Quantum logic
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
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[1] Beltrametti, E. G., and Bugajski, S. (1995a). Quantum observables in classical frameworks,International Journal of Theoretical Physics,34, 1221–1229. · Zbl 0850.81019
[2] Beltrametti, E. G., and Bugajski, S. (1995b). A classical extension of quantum mechanics,Journal of Physics A: Mathematical and General,28, 3329–3343. · Zbl 0859.46049
[3] Beltrametti, E. G., and Bugajski, S. (1996). The Bell phenomenon in classical frameworks,Journal of Physics A: Mathematical and General,29, 247–261. · Zbl 0914.46060
[4] Beltrametti, E. G., and Bugajski, S. (n.d.). Effects algebras and statistical physical theories, submitted. · Zbl 0874.06009
[5] Busch, P., Lahti, P. J., and Mittelstaedt P. (1991).The Quantum Theory of Measurement, Springer-Verlag, Berlin. · Zbl 0868.46051
[6] Dvurečenskij, A. (1993).Gleason’s Theorem and its Applications, Kluwer, Dordrecht and Ister Science Press, Bratislava. · Zbl 0795.46045
[7] Dvurečenskij, A. (n.d.). Fuzzy set representation of some quantum structures,Fuzzy Sets and Systems, to appear.
[8] Foulis D. J., and Bennett, M. K. (1993). Tensor products of orthoalgebras,Order,10, 271–282. · Zbl 0798.06015
[9] Giuntini, R., and Greuling, H. (1989). Toward a formal language for unsharp properties,Foundations of Physics,19, 931–945.
[10] Hausdorff, F. (1921a). Summationsmethoden und Momentfolgen, I.Mathematische Zeitschrift,9, 74–109. · JFM 48.2005.01
[11] Hausdorff, F. (1921b). Summationsmethoden und Momentfolgen, II,Mathematische Zeitschrift,9, 280–299. · JFM 48.2005.02
[12] Hausdorff, F. (1923). Momentprobleme für ein endliches Interval,Mathematische Zeitschrift,16, 220–248. · JFM 49.0193.01
[13] Kadison, R. V. (1952). A generalized Schwarz inequality and algebraic invariants for operators and algebras,Annals of Mathematics,56, 494–503. · Zbl 0047.35703
[14] Kôpka, F., and Chovanec, F. (1994). D-posets,Mathematica Slovaca,44, 21–34. · Zbl 0789.03048
[15] Reed, M., and Simon, B. (1972).Methods of Modern Mathematical Physics I, Functional Analysis, Academic Press, New York. · Zbl 0242.46001
[16] Riesz, F., and Sz.-Nagy, B. (1955).Leçons d’Analyse Fonctionelle, 3rd ed, Akadémiai Kiadó, Budapest.
[17] Shohat, J., and Tamarkin, J. (1943).The Problem of Moments, American Mathemtical Society, Providence, Rhode Island. · Zbl 0063.06973
[18] Widder, D. V. (1946).Laplace Transform, Princeton University Press, Princeton, New Jersey. · Zbl 0060.24801
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