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Foundations of Physics

, Volume 30, Issue 10, pp 1737–1755 | Cite as

Piron's and Bell's Geometric Lemmas and Gleason's Theorem

  • Georges Chevalier
  • Anatolij Dvurečenskij
  • Karl Svozil
Article

Abstract

We study the idea of implantation of Piron's and Bell's geometrical lemmas for proving some results concerning measures on finite as well as infinite-dimensional Hilbert spaces, including also measures with infinite values. In addition, we present parabola based proofs of weak Piron's geometrical and Bell's lemmas. These approaches will not used directly Gleason's theorem, which is a highly non-trivial result.

Keywords

Hilbert Space Geometric Lemma 
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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Georges Chevalier
    • 1
  • Anatolij Dvurečenskij
    • 2
  • Karl Svozil
    • 3
  1. 1.Institut Girard DesarguesVilleurbanneFrance;
  2. 2.Mathematical InstituteSlovak Academy of SciencesBratislavaSlovakia;
  3. 3.Institut für Theoretische PhysikTU WienViennaAustria;

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