Non-linear $\ast$-Jordan triple derivation on prime $\ast$-algebras

Abstract

Let $\mathcal{A}$ be a prime $\ast$-algebra and $\Phi$ preserves triple $\ast$-Jordan derivation on $\mathcal{A}$, that is, for every $A,B\in \mathcal{A}$, $$\Phi (A\diamond B\diamond C)=\Phi (A)\diamond B\diamond C+A\diamond \Phi (B)\diamond C+A\diamond B\diamond \Phi (C)$$ where $A\diamond B=AB+B{A}^{\ast }$ then $\Phi$ is additive. Moreover, if $\Phi (\alpha I)$ is self-adjoint for $\alpha \in \{1,i\}$ then $\Phi$ is a $\ast$-derivation.

12 pages