Nonlinear Derivable Maps On Triangular Algebras And Factor Von Neumann Algebras

In this paper,we mainly study nonlinear Jordan(Lie)derivable maps on triangu-lar algebras by Lie product square zero elements and nonlinear*-Jordan semi-triple derivable maps on factor von Neumann algebras.The details are as follows:In Chapter 1,we give some common symbols,definitions(for example,trian-gular algebra,derivable map,additive*-derivation)and so on.In Chapter 2,we mainly discuss two nonlinear derivable maps on triangular algebras by Lie product square zero elements.Let u= Tri(A,M,B)be a 2-torsion free triangular algebra,and Q = {u?u:u2 = 0}.As applications,the form of local derivable nonlinear maps on upper triangular matrix algebras and nest algebras is obtained.In Chapter 3,we mainly discuss nonlinear*-Jordan semi-triple derivable maps on factor von Neumann algebras.Let A be a factor von Neumann algebra.As applications,the form of nonlinear derivable maps on matrix algebras and the type of I von Neumann algebras is obtained.