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Non-Linear Integration and Signed Measures on Von Neumann Algebras

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Current Issues in Quantum Logic

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Abstract

We present here some partial results on the decomposition problem of signed measures on von Neumann algebras.5 We consider the approach to generalized Jordan and Hahn decompositions given in3. This problem was solved many years ago for the case of linear σ-continuous hermitian functionals on W*-algebras.6

Research supported by M. Sklodowska-Curie Fund grant number 0IP74-01416.

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References

  1. A.M. Gleason, J. Math. Mech. 6, no. 6 (1957), p. 885.

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  2. J. Gunson, Ann. I’Inst. H. Poincaré Sect. A (N.S) 17 (1972), pp. 295–311.

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  3. P.R. Haimos, “Measure Theory”, von Nostrand, New York (1950).

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  4. R. Jajte, A. Paszkiewicz, Studia Mathematicae LXIII, 3 (1978), p. 229.

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  5. P. Kruszynski, Some open problems in noncommutative probability, preprint, (to appear in Proceedings of Colloquium on “Random Fields: Rigorous Results in Statistical Mechanics and QFT”, Esztergom, 1979 ).

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  6. S. Sakai, “C*-algebras and W*-algebras”, Springer-Verlag, Berlin (1971).

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  7. A.N. Sherstnev, Verojatnostnye metody i kibernetika X–XI Izd. KGU Kazan (1974), pp. 68–72, (Russian).

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Author information

Authors and Affiliations

  1. Department of Mathematical Methods in Physics, University of Warsaw, Poland

    Pawel Kruszynski

Authors
  1. Pawel Kruszynski
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Editor information

Editors and Affiliations

  1. University of Genoa, Genoa, Italy

    Enrico G. Beltrametti

  2. Department of Philosophy, University of Toronto, Toronto, Ontario, Canada

    Bas C. van Fraassen

  3. University of Southern California, Los Angeles, California, USA

    Bas C. van Fraassen

  4. Istituto di Scienze Fisiche, Via Benedetto XV, 5, 16132, Genova, Italy

    Enrico G. Beltrametti

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© 1981 Plenum Press, New York

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Kruszynski, P. (1981). Non-Linear Integration and Signed Measures on Von Neumann Algebras. In: Beltrametti, E.G., van Fraassen, B.C. (eds) Current Issues in Quantum Logic. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3228-2_31

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  • DOI: https://doi.org/10.1007/978-1-4613-3228-2_31

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3230-5

  • Online ISBN: 978-1-4613-3228-2

  • eBook Packages: Springer Book Archive

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