Nonlinear $n$-tuple $\lambda$-Jordan $\ast$-derivations on von Neumann algebras
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Abstract
Let $\mathfrak{A}$ be a factor von Neumann algebra and $\Omega$ preserves $n$-tuple $\lambda$-Jordan $\ast$-derivations on $\mathfrak{A}$, that is, for every $A_{1},A_{2},\ldots,A_{n} \in \mathfrak{A}$, \begin{eqnarray*} \Omega(A_{1}\triangleright A_{2}\triangleright\ldots \triangleright A_{n})&=&\Omega(A_{1})\triangleright A_{2}\triangleright\ldots \triangleright A_{n}+A_{1}\triangleright \Omega(A_{2})\triangleright\ldots \triangleright A_{n}\\
&&+\ldots+A_{1}\triangleright A_{2}\triangleright \ldots\triangleright \Omega(A_{n}) \end{eqnarray*} where $A_{i}\triangleright A_{j} = A_{i}A_{j} +\lambda A_{j}A_{i}^{\ast}$ for $\lambda \in \mathbb{R}$, $\lambda \notin \lbrace 0, \pm1 \rbrace$, then $\Omega$ is additive $\ast$-derivation.
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References
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