Non-global nonlinear skew Lie triple derivations on factor von Neumann algebras

Source abstract

<abstract><p>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.</p></abstract>