Nonlinear Maps Preserving Mixed Product on Factors.

Let A and B be two factors with dim A > 4 . In this article, it is proved that a 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, or a conjugate linear ∗ -isomorphism, or the negative of a linear ∗ -isomorphism, or the negative of a conjugate linear ∗ -isomorphism. [ABSTRACT FROM AUTHOR]