Nonlinear maps preserving the second mixed triple η‐*‐product between von Neumann algebras

Abstract

Let and  be two von Neumann algebras , at least one of them has no center abelian projection. Let , be a not necessary linear bijection between two von Neumann algebras satisfying  and  .It is proved that if  is a nonlinear maps preserving the second mixed triple product ,the following conclusion is valid: if ,then is linear isomorphism ,if ,then is the sum of linear  isomorphism and conjugate linear isomorphism.