Maps Preserving Jordan*-product On Von Neumann Algebras

Let η be a non-zero scalar. In this paper, we investigate a bijective map φ from avon Neumann algebra A without central abelian projections onto another von Neumannalgebra satisfying φ(AB+ηBA*)=φ(A)φ(B)+ηφ(B)φ(A)*for all A, B∈A. It isshowed 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.