Nonlinear mixed Jordan triple *-derivations on factors

Abstract

Let $\mathcal{A}$ be a factor with dim$\mathcal{A}\ge 2$. For $A,B\in \mathcal{A}$, define by $[A,B{]}_{\ast }=AB-B{A}^{\ast }$ and $A\bullet B=AB+B{A}^{\ast }$ the new products of $A$ and $B$. In this paper, it is proved that a map $\Phi :\mathcal{A}\to \mathcal{A}$ satisfies $\Phi ([A,B{]}_{\ast }\bullet C)=[\Phi (A),B{]}_{\ast }\bullet C+[A,\Phi (B){]}_{\ast }\bullet C+[A,B{]}_{\ast }\bullet \Phi (C)$ for all $A,B,C\in \mathcal{A}$ if and only if $\Phi$ is an additive $\ast -$derivation.

There was an error in Claim 7 of Theorem 2.4