Nonlinear Maps Preserving the Jordan Triple *-Product on Factor von Neumann Algebras

Let \(\mathcal{A}\) and \(\mathcal{B}\) be two factor von Neumann algebras. For \(A,B \in \mathcal{A}\), define by A,B]_* = AB ? BA* the skew Lie product of A and B. In this article, it is proved that a bijective map \(\Phi :\mathcal{A} \to \mathcal{B}\) satisfies Φ(A,B]_*,C]_*) = Φ(A),Φ(B)]_*,Φ(C)]_* for all \(A,B,C \in \mathcal{A}\) if and only if Φ is a linear *-isomorphism, or a conjugate linear *- isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.