International Journal of Theoretical Physics

, Volume 33, Issue 10, pp 1957–1984 | Cite as

Orthosummable orthoalgebras

  • Eissa D. Habil


We introduce notions of orthosummability andσ-orthosummability for orthoalgebras, which generalize the notions of orthocompleteness andσ-orthocompleteness for orthomodular posets, and we characterize such orthoalgebras in terms of their chains. We also show how to sum an infinite subset of an orthoalgebra, and we prove a generalized associative law for such sums.


Field Theory Elementary Particle Quantum Field Theory Infinite Subset Orthomodular Posets 
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  1. Birkhoff, G., and von Neumann, J. (1936).Annals of Mathematics,37, 823–843.Google Scholar
  2. Cook, T. (1978). The Nikodym-Hahn-Vitali-Saks theorem for states on a quantum logic, InProceedings Conference on Mathematical Foundations of Quantum Theory, Loyola University, New Orleans, Academic Press, New York, pp. 275–286.Google Scholar
  3. D'Andrea, A., and De Lucia, P. (1991).Journal of Mathematical Analysis and Applications,154, 507–522.Google Scholar
  4. D'Andrea, A., De Lucia, P., and Morales, P. (1991).Atti Seminario Matematico i Fisico Universita di Modena,34, 137–158.Google Scholar
  5. Foulis, D., and Bennett, M. (1993). Tensor product of orthoalgebras, preprint.Google Scholar
  6. Foulis, D., and Randall, C. (1972).Journal of Mathematical Physics,13, 1167–1175.Google Scholar
  7. Foulis, D., Greechie, R., and Rüttimann, G. (1992).International Journal of Theoretical Physics,31(5), 789–807.Google Scholar
  8. Greechie, R. (1968).Journal of Combinatorial Theory,4(3), 210–218.Google Scholar
  9. Gudder, S. (1965).Transactions of the American Mathematical Society,119, 428–442.Google Scholar
  10. Gudder, S. (1988).Quantum Probability, Academic Press, Boston.Google Scholar
  11. Habil, E. (1993). Morphisms and pasting of orthoalgebras,Order, submitted.Google Scholar
  12. Halmos, P. (1963).Lectures on Boolean Algebras, Van Nostrand, New York.Google Scholar
  13. Holland, S., Jr. (1970).Proceedings of the American Mathematical Society,24, 716–718.Google Scholar
  14. Kalmbach, G. (1983).Orthomodular Lattices, Academic Press, New York.Google Scholar
  15. Kalmbach, G. (1986).Measures on Hilbert Lattices, World Scientific, Singapore.Google Scholar
  16. Lock, P. (1981). Ph.D. dissertation, University of Massachusetts.Google Scholar
  17. Mackey, G. (1963).The Mathematical Foundation of Quantum Mechanics, Benjamin, New York.Google Scholar
  18. Navara, M., and Rogalewicz, V. (1991).Mathematische Nachrichten,145, 157–168.Google Scholar
  19. Navara, M., and Rüttimann, G. (1991).Expositiones Mathematicae,9, 275–284.Google Scholar
  20. Ramsay, A. (1966).Journal of Mathematics and Mechanics,15(2), 227–234.Google Scholar
  21. Randall, C., and Foulis, D. (1973).Journal of Mathematical Physics,14, 1472–1480.Google Scholar
  22. Randall, C., and Foulis, D. (1981). Operational statistics and tensor products, inInterpretations and Foundations of Quantum Theory, Vol. 5, H. Neumann, ed., Bibliographisches Institut Mannheim, Vienna.Google Scholar
  23. Rüttimann, G. (1989).Canadian Journal of Mathematics,41(6), 1124–1146.Google Scholar
  24. Varadarajan, V. (1962).Communications in Pure and Applied Mathematics,15, 189–217.Google Scholar
  25. Wilce, A., and Feldman, D. (1993).σ-additivity in manuals and orthoalgebras,Order, to appear.Google Scholar
  26. Younce, M. (1987). Ph.D. dissertation, University of Massachusetts.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Eissa D. Habil
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of DenverDenver

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