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Communications in Mathematical Physics

, Volume 205, Issue 1, pp 69–79 | Cite as

On the Embedding of von Neumann Subalgebras

  • H.J. Borchers
Article

Abstract:

For a von Neumann algebra with a cyclic and separating vector it will be shown that the von Neumann subalgebras with the same cyclic vector can uniquely be characterized by one-parametric operator-valued functions obeying a set of conditions. Since the properties contain no reference to the subalgebra these operator-valued functions will be called characteristic functions. On the set of characteristic functions there exists a natural topology under which this set is complete.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • H.J. Borchers
    • 1
  1. 1.Institut für Theoretische Physik der Universität Göttingen, Bunsenstrasse 9,¶D–37073 Göttingen, Germany. E-mail: Borchers@Theorie.Physik.UNI-Goettingen.DEGermany

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