Multiplicative ∗-Lie isomorphisms between factors ✩,✩✩

Let M, N be factors. If Φ :M→N is a multiplicative ∗-Lie isomorphism, then Φ is of the form σ + τ, where σ is a linear ∗-isomorphism, or a conjugate linear ∗-isomorphism, or the negative of a linear ∗-anti-isomorphism, or the negative of a conjugate linear ∗-antiisomorphism of M onto N and τ is a mapping of M into CI = {λI | λ ∈ C} which maps commutators into zero.