Non-linear $\ast$-Jordan derivations on von Neumann algebras

Abstract

Let $\mathcal{A}$ be a factor von Neumann algebra and $\varphi$ be the $\ast$-Jordan derivation on $A$, that is, for every $A,B\in \mathcal{A}$, $\varphi (A{\diamond }_{1}B)=\varphi (A){\diamond }_{1}B+A{\diamond }_1\varphi (B)$ where $A{\diamond }_{1}B=AB+B{A}^{\ast }$, then $\varphi$ is additive $\ast$-derivation.

15 pages, Accepted in Linear and Multilinear Algebra