A generalized imprimitivity theorem for a class of POV — measures

  • S. Twareque Ali
Session VIII — Goemetical Methosds in Quantum Mechanics and Field Theory
Part of the Lecture Notes in Physics book series (LNP, volume 180)


We discuss some recently obtained results on the problem of generalizing the imprimitivity theorem of Mackey, to the case where the underlying projection valued measure is replaced by a commutative positive operator valued measure. A possible extension of the group representation to a K-space is also discussed.


Hilbert Space Probability Measure Topological Space Compact Group Positive Operator 
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  1. 1).
    S.T. Ali, Lecture Notes in Mathematics, Vol. 905, Springer-Verlag, Berlin (1982), pp. 207–228.Google Scholar
  2. 2).
    M. Takesaki, Acta Math. 119 (1967), 273.Google Scholar
  3. 3).
    S.T. Ali,“Commutative systems of covariance and a generalization of Mackey's imprimitivity theorem”, to appear.Google Scholar
  4. 4).
    G.W. Mackey, Proc. Natl. Acad. Sci. U.S.A. 35 (1949), 537.Google Scholar
  5. 5).
    A. Giovannini, J. Math. Phys. 22 (1981), 2389.Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • S. Twareque Ali
    • 1
  1. 1.Department of MathematicsConcordia UniversityMontrÉalCanada

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