Abstract:

Let ${\cal A}$ be a factor von Neumann algebra and $\xi$ be a non-zero complex number. A nonlinear map $\phi:\mathcal A\rightarrow\mathcal A$ has been demonstrated to satisfy $\phi(A\diamond_{\xi}B\diamond_{\xi}C)=\phi(A)\diamond_{\xi}B\diamond_{\xi}C+A\diamond_{\xi}\phi(B)\diamond_{\xi}C+A\diamond_{\xi}B\diamond_{\xi}\phi(C)$ for all $A, B, C\in\mathcal A$ if and only if $\phi$ is an additive *-derivation and $\phi(\xi A)=\xi\phi(A)$ for all $A\in\mathcal A.$

Key words: ξ-Jordan *-triple derivable mapping, von Neumann algebra, *-Derivation