Maps Preserving Projections on von Neumann Algebras

Let (A) be a von Neumann algebra over complex Hilbert space H,and P((A))denote all projections of (A).In this paper,we prove that a continuous surjective mapping Φ:(A)→(A) if satisfies A+λB ∈ P((A))(→)Φ(A)+λΦ(B) ∈ P((A)),(V)A,B ∈ (A) and (V) λ ∈ C,then Φ is a Jordan isomorphism on (A).