Nonlinear Maps Preserving Mixed Jordan Triple Products on von Neumann Algebras

Abstract:

      In this paper, we prove that if a bijective map $\Phi$ preserves mixed Jordan triple products between von Neumann algebras with no central abelian projections, then $\Phi(I)\Phi$ is the sum of a linear $*$-isomorphism and a conjugate linear $*$-isomorphism, where $\Phi(I)$ is a self-adjoint central element in the range with $\Phi(I)^{2}=I$. Also, we give the structure of this map that preserves mixed Jordan triple products between factor von Neumann algebras.