MAPS PRESERVING STRONG SKEW LIE PRODUCT ON FACTOR VON NEUMANN ALGEBRAS

摘要

Let A be a factor von Neumann algebra and Φ be a nonlinear surjective map from A onto itself.We prove that,if Φ satisfies that Φ(A)Φ(B)-Φ(B)Φ(A)= AB-BA* for all A,B ∈ A,then there exist a linear bijective map Ψ:A → A satisfying Ψ(A)Ψ(B)-Ψ(B)Ψ(A)= AB-BA* for A,B ∈A and a real functional h on A with h(0) = 0 such that Φ(A) = Ψ(A) + h(A)I for every A ∈A.In particular,if A is a type I factor,then,Φ(A) = cA + h(A)I for every A ∈ A,where c = ±1.