Nonlinear maps preserving the mixed triple *-product between factors

Abstract

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