Nonlinear Mixed Derivable Maps And Bilocal Lie Derivations On Factor Von Neumann Algebras

In this paper,we mainly study the problems of nonlinear mixed ξ-Jordan triple derivable mappings and bilocal Lie derivations on factor von Neumann algebras.The main contents are as follows:In Chapter 1,we introduce some basic concepts of nonlinear(skew)Jordan triple derivable mapping,additive*-derivation,factor von Neumann algebra and some known theorems to be involved in the article.In Chapter 2,we mainly study nonlinear mixed ξ-Jordan triple derivation on factor von Neumann algebra.Let A be a factor acting on a complex Hilbert space H and φ:A→A be the nonlinear mixed ξ-Jordan triple derivation.We prove that the mapping φ is an additive*-derivation andφ(ξA)=ξφ(A)for any A∈A.In Chapter 3,we mainly characterize bilocal Lie derivations on factors.Let A be a factor acting on a complex separable Hilbert space H with dim(A)>9.We prove that every bilocal Lie derivation on factors is a Lie derivation.