Communications in Mathematical Physics

, Volume 6, Issue 3, pp 194–204 | Cite as

Types of von Neumann algebras associated with extremal invariant states

  • Erling Størmer


A globalized version of the following is proved. Let ℛ be a factor acting on a Hilbert space ℋ,G a group of unitary operators on ℋ inducing automorphisms of ℛ,x a vector separating and cyclic for ℛ which is up to a scalar multiple the unique vector invariant under the unitaries inG. Then either ℛ is of type III or ω x is a trace of ℛ. The theorem is then applied to study the representations due to invariant factors state of asymptotically abelianC*-algebras, and to show that in quantum field theory certain regions in the Minkowski space give type III factors.


Neural Network Statistical Physic Hilbert Space Field Theory Complex System 
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Copyright information

© Springer-Verlag 1967

Authors and Affiliations

  • Erling Størmer
    • 1
  1. 1.Mathematical InstituteUniversity of OsloOsloNorway

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