Communications in Mathematical Physics

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

On the purification of factor states

  • S. L. Woronowicz


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.


Neural Network Purification Statistical Physic Complex System Nonlinear Dynamics 
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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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