| In this paper,we mainly study Lie triple derivations on factor von Neumann algebras and triangular algebras.The details are as follows:In Chapter 1,we give some common symbols,definitions(for example,trian-gular algebras,derivations,inner derivations)and so on.In Chapter 2,we mainly characterize Lie triple derivable maps on factor von Neumann algebras.Let A be a factor von Neumann algebra with dimension greater than 1,in this paper,we prove that if δ:A→A is a linear map satisfying δ([[A,B],C])=[[δ(A),B],C]+[[A,6(B)],C]+[[A,B],δ(C)] for any A,B,C ∈A with AB= AC= 0(resp.AB= AC= P),then there exist an operator T ∈ A and a linear map h:A→ CI vanishing at every second commutator[[A,B],C]with AB = AC = 0(resp.AB = AC = P)such thatδ(A)= AT-TA + h(A)for any A E A.In Chapter 3,we mainly discuss zero product and Jordan zero product Lie triple derivable maps on triangular algebras.Let U = Tri(A,M,B)be a triangular algebra,in this paper,under mild assumptions,we prove that if δ:u → u is a linear map satisfying δ([[U,V],W])=[[δ(U)V],W]+[[U,δ(V)],W]+[[U,V],δ(W)] for any U,V,W ∈ U with UV = UW = 0(resp.UοV = UοW = 0),thenδ(U)= φp(U)+ h(U)for any U∈ U,where φ:u→ u is a derivation,h:u →Z(U)is a linear map vanishing at second commutators with UV = UW = 0(resp.UοV = UοW=0). |
