Characterization of Lie-Type Higher Derivations of von Neumann Algebras with Local Actions
DOI: 10.3390/math11234770
Let m and n be fixed positive integers. Suppose that A is a von Neumann algebra with no central summands of type I1, and Lm: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 phi m:A -> A and an additive higher map zeta m:A -> Z(A), which annihilates every (n-1)th commutator pn(S1,S2,MIDLINE HORIZONTAL ELLIPSIS,Sn) with S1S2=0 such that Lm(S)=phi m(S)+zeta m(S)for all S is an element of A. We also demonstrate that the result holds true for the case of the projection product. Further, we discuss some more related results.
Data mining evaluation is very critical in the sense that it determines how well a classification model performs and how well it can generate accurate predictions on brand-new, unexplored data. It…
Let m and n be fixed positive integers. Suppose that A is a von Neumann algebra with no central summands of type I1, and Lm:A -> A is a Lie-type higher derivation.
A well-known result of Posner's second theorem states that if the commutator of each element in a prime ring and its image under a nonzero derivation are central, then the ring is commutative. In…