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 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.

Automated summary

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.