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 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.