Maps preserving productX*Y + YX* on factor von Neumann algebras

Let 𝒜 and ℬ be two factor von Neumann algebras. In this article, we prove that a nonlinear bijective map Φ : 𝒜 → ℬ satisfies Φ(X* Y + YX*) =Φ(X)*Φ(Y) + Φ(Y)Φ(X)* (∀X, Y ∈ 𝒜), if and only if Φ is a *-ring isomorphism. In particular, if 𝒜 and ℬ are type I factors, then Φ is a unitary isomorphism or conjugate unitary isomorphism.