Strong skew commutativity preserving maps on von Neumann algebras

Let $\mathcal{M}$ be a von Neumann algebra without central summands of type $I_1$. Assume that $\mathrm{\Phi }:\mathcal{M}\to \mathcal{M}$ is a surjective map. It is shown that $\mathrm{\Phi }$ is strong skew commutativity preserving (that is, satisfies $\mathrm{\Phi }(A)\mathrm{\Phi }(B)-\mathrm{\Phi }(B)\mathrm{\Phi }(A{)}^{\ast }=AB-B{A}^{\ast }$ for all $A,B\in{\mathcal M}$)ifandonlyifthereexistssomeself-adjointelement$Z$inthecenterof${\mathcal M}$with$Z^2=I$suchthat$\Phi(A)=ZA$forall$A\in{\mathcal M}$. The strong skew commutativity preserving maps on prime involution rings and prime involution algebras are also characterized.