Characterizations of local Lie derivations on von Neumann algebras

Guangyu An; Xueli Zhang; Jun He; Wenhua Qian; Guangyu An; Xueli Zhang; Jun He; Wenhua Qian

doi:10.3934/math.2022422

AIMS Mathematics

2022, Volume 7, Issue 5: 7519-7527. doi: 10.3934/math.2022422

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Research article

Characterizations of local Lie derivations on von Neumann algebras

Guangyu An ^{1
,
,},
Xueli Zhang ¹,
Jun He ²,
Wenhua Qian ^{3
,
,}

1.
Department of Mathematics, Shaanxi University of Science and Technology, Xi'an 710021, China
2.
Department of Mathematics, Anhui Polytechnic University, Wuhu 241000, China
3.
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

Received: 21 October 2021 Revised: 13 December 2021 Accepted: 21 December 2021 Published: 14 February 2022
MSC : 46L50, 46L57, 47L35

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.
- Lie derivation,
- local Lie derivation,
- von Neumann algebra,
- locally measurable operator
Citation: Guangyu An, Xueli Zhang, Jun He, Wenhua Qian. Characterizations of local Lie derivations on von Neumann algebras[J]. AIMS Mathematics, 2022, 7(5): 7519-7527. doi: 10.3934/math.2022422

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Abstract

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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