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The inner orthogonality of convex sets in axiomatic quantum mechanics

  • U. Krause
Special Topics
Part of the Lecture Notes in Physics book series (LNP, volume 29)

Keywords

Orthogonality Relation Order Vector Space Real Linear Space Convex Hausdorff Topological Vector Space Conventional Quantum Mechanics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alfsen, E.M.: Compact convex sets and boundary integrals Ergebnisse der Mathematik 57, Springer Verlag 1971Google Scholar
  2. 2.
    Ancona, A.: Sur les convexes de Ludwig Ann.Inst.Fourier 2o,2, 21–44 (1970)Google Scholar
  3. 3.
    Bauer, H.: Intern vollständige konvexe Mengen Aarhus Universitet Preprint Series No. 30 1970/71Google Scholar
  4. 4.
    -, Bear,H.S.: The part metric in convex sets Pac.J.Math. 30, 15–33 (1969)Google Scholar
  5. 5.
    Davies, E.B.: The structure and ideal theory of the predual of a Banach lattice. Trans.Amer.Math.Soc. 131, 544–555 (1968)Google Scholar
  6. 6.
    -, Lewis, J.T.: An operational approach to quantum probability Commun.Math.Phys. 17, 139–26o (1970)CrossRefGoogle Scholar
  7. 7.
    Edwards, C.M.: Classes of operations in quantum theory Commun.Math.Phys. 2o, 26–56 (1971)CrossRefGoogle Scholar
  8. 8.
    -, Gerzon, M.A.: Monotone convergence in partially ordered vector spaces. Ann.Inst.Henri Poincaré, 12(4), 323–328 (1970)Google Scholar
  9. 9.
    Ellis, A.J.: Minimal decompositions in base normed spaces This volumeGoogle Scholar
  10. 10.
    Foulis, D.J., Randall, C.H.: Lexicographic orthogonality J.Combinatorial Theory 11, 157–162 (1971)CrossRefGoogle Scholar
  11. 11.
    Gudder, S.: Convex structures and operational quantum mechanics Commun.Math.Phys. 29(3), 249–264 (1973)CrossRefGoogle Scholar
  12. 12.
    Haag, R.: Bemerkungen zum Begriffsbild der Quantenphysik Z.Physik 229, 384–391 (1969)CrossRefGoogle Scholar
  13. 13.
    Hausner, M.: Multidimensional utilities. In: Thrall, R.M., Coombs, C.H., Davis, R.L.(ed.): Decision processes. Wiley 1954Google Scholar
  14. 14.
    Herbut, F.: Derivation of the change of state in measurement from the concept of minimal measurement Annals of Physics 55, 271–300 (1969)CrossRefGoogle Scholar
  15. 15.
    Jauch, J.M., Misra, B., Gibson, A.G.: On the asymptotic condition of scattering theory. Helv.Phys.Acta 41, 513–527 (1968)Google Scholar
  16. 16.
    König, H.: Über das von Neumannsche Minimax — Theorem Arch.Math. 19, 482–487 (1968)CrossRefGoogle Scholar
  17. 17.
    Krause, U.: Der Satz von Choquet als ein abstrakter Spektralsatz und vice versa. Math.Ann. 184, 275–296 (197o)Google Scholar
  18. 18.
    —: Strukturen in unendlichdimensionalen konvexen Mengen ForthcomingGoogle Scholar
  19. 19.
    Ludwig,G.: Deutung des Begriffs “physikalische Theorie” und axiomatische Grundlegung der Hilbertraumstruktur der Quantenmechanik durch Hauptsätze des Messens. Lecture Notes in Physics 4. Springer Verlag 1970Google Scholar
  20. 20.
    —: The measuring and preparing process and macro theory This volumeGoogle Scholar
  21. 21.
    Mielnik, B.: Theory of filters Commun.Math.Phys. 15, 1–46 (1969)CrossRefGoogle Scholar
  22. 23.
    Robinson, D.W.: Normal and locally normal states Commun.Math.Phys. 19, 219–234 (1970)CrossRefGoogle Scholar
  23. 24.
    Schaefer, H.H.: Topological vector spaces. Macmillan 1966Google Scholar
  24. 25.
    Schmidt, H.J.: Die Kategorie der Operationen in der Axiomatischen Quantenmechanik.Typoscript. Marburg 1972Google Scholar
  25. 26.
    Semadeni, Z.: Categorical methods in convexity. In: Proc.Coll.Convexity, 281–3o7, Copenhagen 1967Google Scholar
  26. 27.
    Varadarajan, V.S.: Geometry of quantum theory. Vol.I. Van Nostrand 1968Google Scholar
  27. 28.
    Wils, W.: The ideal center of partially ordered vector spaces Acta mathematica 127, 41–77 (1971)Google Scholar
  28. 29.
    —: Centers and central measures This volumeGoogle Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • U. Krause
    • 1
  1. 1.Fachbereich Mathematik der Universität BremenBremenWest Germany

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