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Communications in Mathematical Physics

, Volume 28, Issue 3, pp 221–235 | Cite as

On the purification of factor states

  • S. L. Woronowicz
Article

Abstract

Let\(\mathfrak{A}\) be aC*-algebra and\(\mathfrak{A}^ \circ \) be an opposite algebra. Notions of exact andj-positive states of\(\mathfrak{A}^ \circ \)\(\mathfrak{A}\) are introduced. It is shown, that any factor state ω of\(\mathfrak{A}\) can be extended to a pure exactj-positive state\(\tilde \omega \) of\(\mathfrak{A}^ \circ \)\(\mathfrak{A}\). The correspondence ω→\(\tilde \omega \) generalizes the notion of the purifications map introduced by Powers and Størmer. The factor states ω1 and ω2 are quasi-equivalent if and only if their purifications\(\tilde \omega _1 \) and\(\tilde \omega _2 \) are equivalent.

Keywords

Neural Network Purification Statistical Physic Complex System Nonlinear Dynamics 
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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References

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Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • S. L. Woronowicz
    • 1
  1. 1.Department of Mathematical Methods of PhysicsUniversity of WarsawWarsawPoland

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