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\(2\)-Local derivations on von Neumann algebras
Preprint
14 February 2014
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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.