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Types of von Neumann algebras associated with extremal invariant states

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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.

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Authors and Affiliations

  1. Mathematical Institute, University of Oslo, Oslo, Norway

    Erling Størmer

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  1. Erling Størmer
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Størmer, E. Types of von Neumann algebras associated with extremal invariant states. Commun.Math. Phys. 6, 194–204 (1967). https://doi.org/10.1007/BF01659976

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  • DOI: https://doi.org/10.1007/BF01659976

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