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2-Local derivations on von Neumann algebras

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Abstract

The paper is devoted to the description of 2-local derivations on von Neumann algebras. Earlier it was proved that every 2-local derivation on a semi-finite von Neumann algebra is a derivation. In this paper, using the analogue of Gleason Theorem for signed measures, we extend this result to type \(III\) von Neumann algebras. This implies that on arbitrary von Neumann algebra each 2-local derivation is a derivation.

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Acknowledgments

The authors are indebted to the referee for the valuable comments.

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Authors and Affiliations

  1. Institute of Mathematics, National University of Uzbekistan, Dormon yoli 29, Tashkent, 100125, Uzbekistan

    Shavkat Ayupov

  2. The Abdus Salam International Centre For Theoretical Physics (ICTP), Trieste, Italy

    Shavkat Ayupov

  3. Department of Mathematics, Karakalpak State University, Ch. Abdirov 1, Nukus, 230113, Uzbekistan

    Karimbergen Kudaybergenov

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  1. Shavkat Ayupov
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  2. Karimbergen Kudaybergenov
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Correspondence to Karimbergen Kudaybergenov.

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Ayupov, S., Kudaybergenov, K. 2-Local derivations on von Neumann algebras. Positivity 19, 445–455 (2015). https://doi.org/10.1007/s11117-014-0307-3

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  • DOI: https://doi.org/10.1007/s11117-014-0307-3

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