Jordan Derivable Mappings at Zero Point

摘要

Let β be an arbitrary non-trivial nest in any factor von Neumann algebra M; and Φ: algMβ→M be a weakly continuous linear mapping. We say that Φ is a Jordan derivable mapping at zero point if Φ(AB + BA) = Φ(A)B + AΦ(B) +Φ(B)A + BΦ(A) for all A,B∈Α with AB + BA = 0. In this paper, we prove that if Φ is a Jordan derivable mapping at zero point, then there exist a derivation δ:algMβ→M and a scalar λ∈C such that Φ(A)=δ(A) +λA for all A in algMβ.