$2$-Local derivations on von Neumann algebras

Shavkat Ayupov; Karimbergen Kudaybergenov

doi:10.1007/s11117-014-0307-3

$2$-Local derivations on von Neumann algebras

Operator Algebras 2014-10-07 v1

Authors: 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.

Keywords

2-local derivations von Neumann algebras Gleason Theorem signed measures type III von Neumann algebras semi-finite algebras

Cite

@article{arxiv.1402.3368,
  title  = {$2$-Local derivations on von Neumann algebras},
  author = {Shavkat Ayupov and Karimbergen Kudaybergenov},
  journal= {arXiv preprint arXiv:1402.3368},
  year   = {2014}
}

Comments

7 pages

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