Characterizations of local Lie derivations on von Neumann algebras

In this paper, we prove that every local Lie derivation on von Neumann algebras is a Lie derivation; and we show that if $ \mathcal M $ is a type I von Neumann algebra with an atomic lattice of projections, then every local Lie derivation on $ LS(\mathcal M) $ is a Lie derivation.

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Bibliographic Details
Published inAIMS mathematics Vol. 7; no. 5; pp. 7519 - 7527
Main Authors An, Guangyu, Zhang, Xueli, He, Jun, Qian, Wenhua
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
lie derivation
local lie derivation
locally measurable operator
von neumann algebra
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ISSN2473-6988
2473-6988
DOI10.3934/math.2022422

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Summary:In this paper, we prove that every local Lie derivation on von Neumann algebras is a Lie derivation; and we show that if $ \mathcal M $ is a type I von Neumann algebra with an atomic lattice of projections, then every local Lie derivation on $ LS(\mathcal M) $ is a Lie derivation.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2022422