Strong skew commutativity preserving maps on von Neumann algebras

Let M be a von Neumann algebra without central summands of type I 1 . Assume that Φ : M → M is a surjective map. It is shown that Φ is strong skew commutativity preserving (that is, satisfies Φ ( A ) Φ ( B ) − Φ ( B ) Φ ( A ) ∗ = A B − B A ∗ for all A , B ∈ M ) if and only if there exists some self-adjoint element Z in the center of M with Z 2 = I such that Φ ( A ) = Z A for all A ∈ M . The strong skew commutativity preserving maps on prime involution rings and prime involution algebras are also characterized.