Let A be a von Neumann algebra acting on the complex Hilbert space H and :A −→ A be a surjective map that satisfies the condition (T )(P) + (P)(T ) ∗ = T P + PT∗ for all T and all projections P in A. We characterize the concrete form of on selfadjoint elements of A. Also when A is a factor von Neumann algebra, it is shown that is either of the form (T ) = T + iτ(T )I or of the form (T ) = −T + iτ(T )I, where τ :A −→ R is a real map.
