Let $ \mathcal{A} $ be a factor von Neumann algebra acting on a complex Hilbert space $ H $ with dim $ \mathcal{A} > 1 $. We prove that if a map $ \delta: \mathcal{A}\rightarrow \mathcal{A} $ satisfies $ \delta([[A, B]_{\ast}, C]_{\ast}) = [[\delta(A), B]_{\ast}, C]_{\ast}+[[A, \delta(B)]_{\ast}, C]_{\ast} +[[A, B]_{\ast}, \delta(C)]_{\ast} $ for any $ A, B, C\in \mathcal{A} $ with $ A^{\ast}B^{\ast}C = 0 $, then $ \delta $ is an additive $ \ast $-derivation.
Citation: Liang Kong, Chao Li. Non-global nonlinear skew Lie triple derivations on factor von Neumann algebras[J]. AIMS Mathematics, 2022, 7(8): 13963-13976. doi: 10.3934/math.2022771
Let $ \mathcal{A} $ be a factor von Neumann algebra acting on a complex Hilbert space $ H $ with dim $ \mathcal{A} > 1 $. We prove that if a map $ \delta: \mathcal{A}\rightarrow \mathcal{A} $ satisfies $ \delta([[A, B]_{\ast}, C]_{\ast}) = [[\delta(A), B]_{\ast}, C]_{\ast}+[[A, \delta(B)]_{\ast}, C]_{\ast} +[[A, B]_{\ast}, \delta(C)]_{\ast} $ for any $ A, B, C\in \mathcal{A} $ with $ A^{\ast}B^{\ast}C = 0 $, then $ \delta $ is an additive $ \ast $-derivation.
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Liang Kong, Chao Li. Non-global nonlinear skew Lie triple derivations on factor von Neumann algebras[J]. AIMS Mathematics, 2022, 7(8): 13963-13976. doi: 10.3934/math.2022771
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