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Communications in Mathematical Physics

, Volume 30, Issue 1, pp 55–67 | Cite as

On the purification map

  • S. L. Woronowicz
Article

Abstract

The investigation of purifications of factor states has been carried on. It is shown, that any factor state θ of aC*-algebra admits at most one purification\(\tilde \omega\), so one can introduce the purification map\(\phi :\phi (\omega ) = \tilde \omega\). It turns out, that the Powers and Størmer inequality is valid in this general situation.

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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    Powers, R. T., Størmer, E.: Free states of the canonical anticommutation relations. Commun. math. Phys.16, 1–33 (1970).Google Scholar
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    Schwartz, J.T.:W*-algebras. New York: Gordon and Breach 1967.Google Scholar
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    Takesaki, M.: Tomita's theory of modular Hilbert algebras and its applications. Lecture Notes in Mathematics, Vol. 128. Berlin-Heidelberg-New York: Springer 1970Google Scholar
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    Woronowicz, S. L.: On the purification of factor states. Commun. math. Phys.28, 221–235 (1972).Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

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

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