Characterizations of non-additive mixed skew and $\eta$-Jordan triple higher derivations on prime $\ast$-algebras

Abstract

This article studied the structure of non-additive mixed skew and $\eta$-Jordan triple higher derivations $\Psi=\{\psi_n\}_{n\in \mathbb{N}}$ of $\ast$-algebras $\mathcal{A}$ and proved that under some conditions each non-additive mixed skew and $\eta$-Jordan triple higher derivation $\Psi=\{\psi_n\}_{n\in \mathbb{N}}$ is an additive $\ast$-higher derivation and $\psi_n(\eta x)=\eta\psi_n(x)$ for $-1\neq \eta\in \mathbb{R}$. As applications, non-additive mixed skew and $\eta$-Jordan triple higher derivations on some classical operator algebras are characterized, such that factor von Neumann algebras, standard operator algebras and so on.