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 Phi : M -> M is a surjective map. It is shown that Phi is strong skew commutativity preserving (that is, satisfies Phi(A)Phi(B) - Phi(B)Phi(A)(*) = AB - BA(*) for all A, B is an element of M) if and only if there exists some self-adjoint element Z in the center of M with Z(2) = I such that Phi(A) = ZA for all A is an element of M. The strong skew commutativity preserving maps on prime involution rings and prime involution algebras are also characterized. (C) 2012 Published by Elsevier Inc.