Automorphisms of central extensions of type I von Neumann algebras

Tom 207 / 2011

Sergio Albeverio, Shavkat Ayupov, Karimbergen Kudaybergenov, Rauaj Djumamuratov Studia Mathematica 207 (2011), 1-17 MSC: Primary 46L40; Secondary 46L51, 46L52. DOI: 10.4064/sm207-1-1

Streszczenie

Given a von Neumann algebra $M$ we consider its central extension $E(M)$. For type I von Neumann algebras, $E(M)$ coincides with the algebra $LS(M)$ of all locally measurable operators affiliated with $M.$ In this case we show that an arbitrary automorphism $T$ of $E(M)$ can be decomposed as $T=T_a\circ T_\phi ,$ where $T_a(x)=axa^{-1}$ is an inner automorphism implemented by an element $a\in E(M),$ and $T_\phi $ is a special automorphism generated by an automorphism $\phi $ of the center of $E(M).$ In particular if $M$ is of type I$_\infty $ then every band preserving automorphism of $E(M)$ is inner.

Autorzy

  • Sergio AlbeverioInstitut für Angewandte Mathematik and HCM
    Rheinische Friedrich-Wilhelms-Universität Bonn
    53115 Bonn, Germany
    e-mail
  • Shavkat AyupovInstitute of Mathematics and Information Technologies
    Uzbekistan Academy of Sciences
    100125 Tashkent, Uzbekistan
    and
    Abdus Salam International Centre
    for Theoretical Physics (ICTP)
    Trieste, Italy
    e-mail
  • Karimbergen KudaybergenovKarakalpak State University
    230113 Nukus, Uzbekistan
    e-mail
  • Rauaj DjumamuratovKarakalpak State University
    230113 Nukus, Uzbekistan
    e-mail

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