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Derivations on the algebra of measurable operators affiliated with a type I von Neumann algebra

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Abstract

Let M be a type I von Neumann algebra with the center Z and let LS(M) be the algebra of all locally measurable operators affiliated with M. We prove that every Z-linear derivation on LS(M) is inner. In particular, all Z-linear derivations on the algebras of measurable and respectively totally measurable operators are spatial and implemented by elements of LS(M).

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Bonn, Bonn, D-53115, Germany

    S. Albeverio

  2. Institute of Mathematics and Information Technologies, Tashkent, 100125, Uzbekistan

    Sh. A. Ayupov & K. K. Kudaybergenov

Authors
  1. S. Albeverio
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  2. Sh. A. Ayupov
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  3. K. K. Kudaybergenov
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Correspondence to S. Albeverio.

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The text was submitted by the authors in English.

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Albeverio, S., Ayupov, S.A. & Kudaybergenov, K.K. Derivations on the algebra of measurable operators affiliated with a type I von Neumann algebra. Sib. Adv. Math. 18, 86–94 (2008). https://doi.org/10.3103/S1055134408020028

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  • DOI: https://doi.org/10.3103/S1055134408020028

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