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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
Article

Abstract

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.

Keywords

Neural Network Statistical Physic Hilbert Space Field Theory Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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