• Part III. Invited Papers Dedicated To The Memory Of Charles H. Randall (1928–1987)
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Quantum measure spaces

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Abstract

In this article I present some material of a forthcoming book with the titleQuantum Measures and Spaces. The main theme are generalizations of Gleason's theorem and spaces in which quantum measures exist. Characterizations of such spaces and classifications of their measures are given. The book will contain some supplementary results from the “orthomodular” theory under the heading “Miscellaneous.” It is a sequel to the bookMeasures and Hilbert Lattices of the same author.

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References

  1. 1.

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

    Google Scholar 

  2. 2.

    G. Kalmbach,Measures and Hilbert Lattices (World Scientific, Singapore, 1986).

    Google Scholar 

  3. 2a

    G. Kalmbach, “Quantum measure spaces,” partial Lecture Notes, University of Ulm.

  4. 3.

    H. Keller, “Ein nicht-klassischeer Hilbertscher Raum,”Math. Z. 172, 41–49 (1980).

    Google Scholar 

  5. 3a

    H. Keller, “Measures on orthomodular vector space lattices,”Stud. Math. 88, 183–195 (1988).

    Google Scholar 

  6. 4.

    H. Gensheimer, “Eine verbandstheoretische Charakterisierung von Hilberträumen,” Master's Thesis, University of Ulm, 1980.

  7. 5.

    H. Gross and U. Künzi, “On a class of orthomodular quadratic spaces,”L'Enseign. Math. 31, 187–212 (1985).

    Google Scholar 

  8. 6.

    H. Gross,Quadratic Forms in Infinite-dimensional Vector Spaces (Birkhäuser, Basel, 1979).

    Google Scholar 

  9. 7.

    H. Gross, “Different orthomodular orthocomplementations on a lattice,”Order 4, 79–92 (1987).

    Google Scholar 

  10. 8.

    U. Künzi, “Orthomodulare Räume über bewerteten Körpern,” Ph.D. Thesis, University of Zürich, 1984.

  11. 9.

    A. Fässler-Ullmann, “On nonclassical Hilbert spaces,”Expo. Math. 3, 275–277 (1983).

    Google Scholar 

  12. 10.

    B. H. Neumann, “On ordered division rings,”Trans. Am. Math. Soc. 66, 202–252 (1949).

    Google Scholar 

  13. 11.

    P. Ribenboim, “Theorie des valuations” (Les Presses de l'Université de Montreal, 1965).

  14. 12.

    H. Keller, “Masstheorie auf orthomodularen Verbänden,” Lecture Notes, University of Zürich, 1988/1989.

  15. 13.

    A. Dvurecenskij, “Generalization of Maeda's theorem,”Int. J. Theor. Phys. 25, 1117–1124 (1986).

    Google Scholar 

  16. 14.

    A. Dvurecenskij and L. Misik, “Gleason's theorem and completeness of inner product spaces,”Int. J. Theor. Phys. 27, 417–426 (1988).

    Google Scholar 

  17. 15.

    S. Maeda, “Probability measures on projections in von Neumann algebras,” preprint,Reviews Math. Phys. 7, 235–290 (1990).

    Google Scholar 

  18. 16.

    E. Christensen, “Measures on projections and physical states.”Comment. Math. Phys. 86, 529–538 (1982).

    Google Scholar 

  19. 17.

    E. Christensen, Comment my paper “Measures on projections and physical states,” Preprint, 1985.

  20. 18.

    F. Yeadon, “Measures on projections inW*-algebras of type II1,”Bull. London Math. Soc. 15, 139–145 (1983).

    Google Scholar 

  21. 19.

    F. Yeadon, “Finitely additive measures on projections in finiteW*-algebras,”Bull. London Math. Soc. 16, 145–150 (1984).

    Google Scholar 

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Kalmbach, G. Quantum measure spaces. Found Phys 20, 801–821 (1990). https://doi.org/10.1007/BF01889692

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Keywords

  • Main Theme
  • Measure Space
  • Quantum Measure
  • Supplementary Result
  • Forthcoming Book