Non-linear λ−jordan Triple∗−derivation on Prime ∗−algebras

Abstract

Let $\mathcal{A}$ be a prime $\ast-$algebra and $\Phi$ a $\lambda-$Jurdan triple derivation on A, that is, for every $A, B, C \in \mathcal{A}$, $\Phi(A\diamond B)=\Phi(A)\diamond B+ A\diamond\Phi(B)$ wher $A\diamond_\lambda B = AB^\ast +\lambda BA$ such that a real scalar $|\lambda|\ne 0, 1,$ and $\Phi$ is additive. moreover, if $\Phi(I)$ and $\Phi(il)$ are selfadjiont then $\Phi$ is a $\ast-$derivation.