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Generalization of Maeda's theorem

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Abstract

The theorem of S. Maeda concerning the characterization of finite measures on a quantum logic of all closed subspaces of a Hilbert space of dimension ≠2 is generalized to the case ofσ-finite measures with possible infinite values. The proof does not involve Gleason's result, but only the proposition on frame functions.

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References

  • Cooke, R., Keane, M., and Moran, W. (1985). An elementary proof of Gleason's theorem,Mathematical Proceedings of the Cambridge Philosophical Society,98, 117–128.

    Google Scholar 

  • Drisch, T. (1979). Generalization of Gleason's theorem,International Journal of Theoretical Physics,18, 239–243.

    Google Scholar 

  • Dvurečenskij, A. (1985). Gleason theorem for signed measures with infinite values,Mathematica Slovaca,35, 319–325.

    Google Scholar 

  • Eilers, M., and Horst, E. (1975). The theorem of Gleason for nonseparable Hilbert space,International Journal of Theoretical Physics,13, 419–424.

    Google Scholar 

  • Gleason, A. M. (1957). Measures on the closed subspaces of a Hilert space,Journal of Mathematics and Mechanics,6, 885–893.

    Google Scholar 

  • Gudder, S. P. (1972). Plane frame functions and pure states in Hilbert spaceInternational Journal of Theoretical Physics,6, 369–375.

    Google Scholar 

  • Kalmbach, G. (1983).Orthomodular Lattices, Academic Press, London.

    Google Scholar 

  • Lugovaja, G. D. (1983). Bilinear forms determining measures on projectors,Izvestija Vuzov-Matematika,1983 (2), 88–88 (in Russian).

    Google Scholar 

  • Lugovaja, G. D., and Sherstnev, A. N. (1980). On the Gleason theorem for unbounded measures,Izvestija Vuzov-Matematika,1980 (12), 30–32 (in Russian).

    Google Scholar 

  • Maeda, S. (1980).Lattice Theory and Quantum Logic, Mahishoten, Tokyo (in Japanese).

    Google Scholar 

  • Maljugin, S. A. (1982). On Gleason's theorem,Izvestija Vuzov-Matematika,1980 (8), 50–51 (in Russian).

    Google Scholar 

  • Schatten, R. (1970).Norm Ideals of Completely Continuous Operators, 2nd ed., Springer-Verlag, Berlin.

    Google Scholar 

  • Ulam, S. (1930). Zur Masstheorie in der allgemeinen Mengelehre,Fundamenta Mathematica,16, 140–150.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Measurement and Measuring Techniques CEPR, Slovak Academy of Sciences, 842 19, Bratislava, Czechoslovakia

    Anatolij Dvurečenskij

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  1. Anatolij Dvurečenskij
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Dvurečenskij, A. Generalization of Maeda's theorem. Int J Theor Phys 25, 1117–1124 (1986). https://doi.org/10.1007/BF00671687

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  • DOI: https://doi.org/10.1007/BF00671687

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