Maps preserving products XY-YX* on von Neumann algebras

Let M, N be von Neumann algebras with no central summands of type I-1. For T, S is an element of M. define [T, S]* = TS - ST* a new product of T and S. In this note, it is proved that a not necessarily linear bijective map Phi : M -> N satisfies Phi([T, S](*)) = [Phi(T), Phi(S)](*) for all T, S is an element of M if and only if Phi is the direct sum of a linear *-isomorphism and a conjugate linear *-isomorphism. (C) 2011 Elsevier Inc. All rights reserved.