Abstract: | Let η be a non-zero scalar. In this paper, we investigate a bijective map ? between two von Neumann algebras, one of which has no central abelian projections, satisfying ?(AB+ηBA∗)=?(A)?(B)+η?(B)?(A)∗ for all A,B in the domain. It is showed that ? is a linear *-isomorphism if η is not real and ? is a sum of a linear *-isomorphism and a conjugate linear *-isomorphism if η is real. |