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