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Communications in Mathematical Physics

, Volume 22, Issue 1, pp 44–50 | Cite as

Vecteurs totalisateurs d'une algèbre de von Neumann

  • J. Dixmier
  • O. Maréchal
Article

Abstract

We prove that the set of cyclic vectors for a von Neumann algebra in a Hilbert spaceH is aGδ set, which is empty or dense. We obtain some corollaries, for instance: if (A1,A2 ...) is a sequence of von Neumann algebras inH, and if eachAn has a cyclic vector and a separating vector, then there exists a vector inH which is cyclic and separating for eachAn. For algebras of local observables, we improve the known results connecting the infinite type of the algebras and the existence of cyclic and separating vectors.

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Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • J. Dixmier
    • 1
  • O. Maréchal
    • 1
    • 2
  1. 1.Université de Paris VIFrance
  2. 2.Résidence Ronsard94 L'Hay-les-RosesFrance

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