2-Local derivations on von Neumann algebras

By Sh. A. Ayupov, K. Kudaybergenov. 2014

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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 $$III$$III von Neumann algebras. This implies that on arbitrary von Neumann algebra each 2-local derivation is a derivation.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dd22d8d1e6791ef8127846ffedcf9ddc262660a2