Integral Equations and Operator Theory

, Volume 34, Issue 2, pp 165–186 | Cite as

The Weyl group and the normalizer of a conditional expectation

  • M. Argerami
  • D. Stojanoff
Article
  • 40 Downloads

Abstract

We define a discrete groupW(E) associated to a faithful normal conditional expectationE : M → N forNM von Neuman algebras. This group shows the relation between the unitary groupUN and the normalizerNE ofE, which can be also considered as the isotropy of the action of the unitary groupUM ofM onE. It is shown thatW(E) is finite if dimZ(N)<∞ and bounded by the index in the factor case. Also sharp bounds of the order ofW(E) are founded.W(E) appears as the fibre of a covering space defined on the orbit ofE by the natural action of the unitary group ofM. W(E) is computed in some basic examples.

AMS Classification Numbers

46L10 46L99 

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Copyright information

© Birkhäuser Verlag 1999

Authors and Affiliations

  • M. Argerami
    • 1
  • D. Stojanoff
    • 2
  1. 1.Dpto. de Matemática Fac. Cs. ExactasUNLPLa PlataArgentina
  2. 2.Instituto Argentino de MatemáticaBuenos AiresArgentina

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