Nonlinear maps preserving Jordan triple η-⁎-products

Abstract

Let η≠−1 be a non-zero complex number, and let ϕ be a not necessarily linear bijection between two von Neumann algebras, one of which has no central abelian projections, satisfying ϕ(I)=I and preserving the Jordan triple η-⁎-product. It is showed that ϕ is a linear ⁎-isomorphism if η is not real and ϕ is the sum of a linear ⁎-isomorphism and a conjugate linear ⁎-isomorphism if η is real.