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arXiv · 1402.3368

$2$-Local derivations on von Neumann algebras

Shavkat Ayupov·Karimbergen Kudaybergenov
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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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Shavkat Ayupov, Karimbergen Kudaybergenov. 2014-02-14. $2$-Local derivations on von Neumann algebras. https://doi.org/10.1007/s11117-014-0307-3

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