Multiplicative biskew Lie triple derivations on factor von Neumann algebras

Abstract

Let $\mathcal{𝒜}$ be a factor von Neumann algebra. For any $\mathcal{𝒜},\mathcal{ℬ}\in \mathcal{𝒜}$, a product ${[\mathcal{𝒜},\mathcal{ℬ}]}_{•}=\mathcal{𝒜}{\mathcal{ℬ}}^{\ast }-\mathcal{ℬ}{\mathcal{𝒜}}^{\ast }$ is called a biskew Lie product. We show that every biskew Lie triple derivation $\psi :\mathcal{𝒜}\to \mathcal{𝒜}$ is an additive $\ast$-derivation.