Maps preserving products XY−YX⁎ on von Neumann algebras

Let M, N be von Neumann algebras with no central summands of type I1. For T,S∈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 Φ:M→N satisfies Φ([T,S]⁎)=[Φ(T),Φ(S)]⁎ for all T,S∈M if and only if Φ is the direct sum of a linear ⁎-isomorphism and a conjugate linear ⁎-isomorphism.