Nonlinear maps preserving the mixed triple ∗-product between factors

Fangjuan Zhang

Let A and B be two factors. In this paper, it is proved that a not necessarily linear bijective map ϕ : A → B satisfies ϕ([A, B] * • C) = [ϕ(A), ϕ(B)] * • ϕ(C) for all A, B, C ∈ A if and only if ϕ is a linear *-isomorphism, a conjugate linear *-isomorphism, the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.