Non-Linear Bi-Skew Jordan Derivations on ∗-Algebra

Abstract

Let $\mathcal{A}$ be a $\ast$-algebra. In this paper, we suppose that $\Phi:\mathcal{A}\to\mathcal{A}$ satisfies$$\Phi(A\diamond B)=\Phi(A)\diamond B+A\diamond\Phi(B)$$where $A\diamond B = A^{*}B + B^{*}A$ for all $A,B\in\mathcal{A}$. Then, $\Phi$ is additive $\ast$-derivation.