Nonlinear maps preserving Lie products on factor von Neumann algebras Original Research Article

In this paper, we prove that every bijective map preserving Lie products from a factor von Neumann algebra image into another factor von Neumann algebra image is of the form A→ψ(A)+ξ(A), where image is an additive isomorphism or the negative of an additive anti-isomorphism and image is a map with ξ(AB-BA)=0 for all image.