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arXiv · 1110.1557

Local and 2-Local derivations on noncommutative Arens algebras

Sh. A. Ayupov·K. K. Kudaybergenov·B. O. Nurjanov·A. K. Alauatdinov
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Abstract

The paper is devoted to so-called local and 2-local derivations on the noncommutative Arens algebra $L^ω(M, τ)$ associated with a von Neumann algebra $M$ and a faithful normal semi-finite trace $τ.$ We prove that every 2-local derivation on $L^ω(M, τ)$ is a spatial derivation, and if $M$ is a finite von Neumann algebra, then each local derivation on $L^ω(M, τ)$ is also a spatial derivation and every 2-local derivation on $M$ is in fact an inner derivation.

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BibTeXRIS

Sh. A. Ayupov, K. K. Kudaybergenov, B. O. Nurjanov, A. K. Alauatdinov. 2011-10-07. Local and 2-Local derivations on noncommutative Arens algebras. https://arxiv.org/abs/1110.1557

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