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| Lie Triple Derivations on von Neumann Algebras |
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Citation： |
Lei LIU.Lie Triple Derivations on von Neumann Algebras[J].Chinese Annals of Mathematics B,2018,39(5):817~828 |
| Page view： 1115
Net amount： 964 |
Authors： |
Lei LIU; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11401452) and the China Postdoctoral
Science Foundation (No.2015M581513). |
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| Abstract： |
Let $\mathcal{A}$ be a von Neumann algebra with no central abelian
projections. It is proved that if an additive map $\delta:
\mathcal{A}\rightarrow \mathcal{A}$ satisfies $\delta([[a, b],
c])=[[\delta(a), b], c]+[[a, \delta(b)], c]+[[a, b], \delta(c)]$ for
any $a, b, c\in \mathcal{A}$ with $ab=0$ (resp. $ab=P$, where $P$ is
a fixed nontrivial projection in $\mathcal{A}$), then there exist an
additive derivation $d$ from $\mathcal{A}$ into itself and an
additive map $f:\mathcal{A}\rightarrow \mathcal{Z}_{\mathcal{A}}$
vanishing at every second commutator $[[a, b], c]$ with $ab=0$
(resp. $ab=P$) such that $\delta(a)=d(a)+f(a)$ for any $a\in
\mathcal{A}$. |
Keywords： |
Derivations, Lie triple derivations, von Neumann algebras |
Classification： |
16W25, 47B47 |
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