Nonlinear $\ast$-Jordan-type derivations on alternative $\ast$-algebras

Abstract

Let $A$ be an unital alternative $\ast$-algebra. Assume that $A$ contains a nontrivial symmetric idempotent element $e$ which satisfies $xA\cdot e=0$ implies $x=0$ and $xA\cdot (1_A-e)=0$ implies $x=0$. In this paper, it is shown that $\Phi$ is a nonlinear $\ast$-Jordan-type derivation on A if and only if $\Phi$ is an additive $\ast$-derivation. As application, we get a result on alternative $W^{\ast }$-algebras.

arXiv comment18 pages