부산대학교 도서관

Let m and n be fixed positive integers. Suppose that A is a von Neumann algebra with no central summands of type I 1 , and L m : A → A is a Lie-type higher derivation. In continuation of the rigorous and versatile framework for investigating the structure and properties of operators on Hilbert spaces, more facts are needed to characterize Lie-type higher derivations of von Neumann algebras with local actions. In the present paper, our main aim is to characterize Lie-type higher derivations on von Neumann algebras and prove that in cases of zero products, there exists an additive higher derivation ϕ m : A → A and an additive higher map ζ m : A → Z (A) , which annihilates every (n − 1) t h commutator p n (S 1 , S 2 , ⋯ , S n) with S 1 S 2 = 0 such that L m (S) = ϕ m (S) + ζ m (S) f o r a l l S ∈ A. We also demonstrate that the result holds true for the case of the projection product. Further, we discuss some more related results. [ABSTRACT FROM AUTHOR]