A result on nonlinear maps preserving mixed Jordan triple <italic>η</italic>-*-product on factor von Neumann algebras.

Abstract<bold>In this paper, it is shown that every nonlinear bijective map <italic>ψ</italic> preserving mixed Jordan triple <italic>η</italic>-products with</bold> η≠−1 <bold>from a factor von Neumann algebra</bold> M <bold>with dim</bold> M>1 <bold>into another factor von Neumann algebra</bold> N <bold>with dim</bold> N>1 <bold>is additive. Also, for</bold> α∈{−1,1} <bold>, we establish that</bold> αψ <bold>is a linear *-isomorphism, and is a conjugate linear *-isomorphism only when</bold> η∈R . [ABSTRACT FROM AUTHOR]