Journal
AIMS MATHEMATICS
Volume 7, Issue 5, Pages 7519-7527Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.2022422
Keywords
Lie derivation; local Lie derivation; von Neumann algebra; locally measurable operator
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Funding
- National Natural Science Foundation of China [11801342, 11801005, 11801050]
- Natural Science Foundation of Chongqing [cstc2020jcyj-msxmX0723]
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In this paper, it is proven that every local Lie derivation on von Neumann algebras is a Lie derivation; and it is shown that if M is a type I von Neumann algebra with an atomic lattice of projections, then every local Lie derivation on LS(M) is a Lie derivation.
In this paper, we prove that every local Lie derivation on von Neumann algebras is a Lie derivation; and we show that if M is a type I von Neumann algebra with an atomic lattice of projections, then every local Lie derivation on LS (M) is a Lie derivation.
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