CLC number: O177

Nonlinear Mixed Jordan Triple *-Higher Derivations on *-Algebras

*-代数上的非线性混合Jordan三重*-高阶导子

School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710062, Shaanxi, China

^† Corresponding author. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 16 January 2025

Abstract

Let $\mathcal{A}$ be a unital $*$-algebra containing a nontrivial projection, $\mathbb{N}$ be the set of non-negative integers. Under some mild conditions on $\mathcal{A}$, it is shown that any nonlinear mixed Jordan triple $*$-higher derivation $\mathcal{D}=\{d_n{\}}_{n\in \mathbb{N}}$ is an additive $*$-higher derivation. In particular, we apply the above result to prime $*$-algebras and von Neumann algebras with no central summands of type $I_{\mathrm{1}}$.

摘要

设$\mathcal{A}$是一个包含非平凡投影和单位元的$*$-代数，$\mathbb{N}$是非负整数集。在满足一定条件的$\mathcal{A}$上，我们证明了任意非线性混合Jordan三重$*$-高阶导子$\mathcal{D}={\left\{d_n\right\}}_{n\in \mathbb{N}}$都是可加的$*$-高阶导子。同时作为应用，我们将这一结论运用到了素$*$-代数和无$I_{\mathrm{1}}$型中心直和项的von Neumann代数。