| Recently,the map without additivity and linearity assumping has been an im-portant issues.In this paper,we introduce and mainly study the characterization of nonlinear mixed Lie triple derivable mappings and nonlinear*ζ-Lie derivable mappings on factors.In Chapter 1,we give some common definitions of factor von Neumann algebras,nonlinear mixed Lie triple derivable mappings,nonlinear*ζ-Lie derivable mappings and so on.In Chapter 2,we mainly discuss nonlinear mixed Lie triple derivable mappings on factors.Let A be a factor von Neumann with dimension greater than 1.We prove that every mapping δ:A→ A satisfies δ([[A,B]*,C])=[[δ(A),B]*,C]+[[A,δ(B)]*,C]+[[A,B]*,δ(C)]for any A,B,C ∈A,then is an additivve-derivation.In Chapter 3,we mainly characterize nonlinear*ζ-Lie derivable mappings on factors.Let A be a factor with dim(A)>1 and ζ ≠ 1.We prove that every mappingδ:A→ A satisfies δ([A*,B]ζ)＝[δ(A)*,B]ζ +[A*,δ(B)]ζ for any A,B ∈A,then δis an additive*-derivation and δ(ζA):ζδ(A). |
