Jordan And Lie Triple Derivable Maps On Nest Algebras

This thesis is devoted to the investigation of Jordan and Lie triple derivable maps on nest algebras.It consists of four chapters.In Chapter 1, we introduce some termi-nology and notation,and summarize the background and state the main contents of this paper；It is proved in Chapter 2 that Lie triple derivable maps on nest algebras are proper；In Chapter 3,we prove that Jordan derivable maps on nest algebras are additive,and that Jordan derivable maps on nest algebras are additive derivations；In Chapter 4,we show that derivable maps on nest algebras are additive.Our main results in this thesis read as follows.1. Let N be a non-trivial nest on Hilbert space H. Suppose that the mapδ: A1gN→B(H)satisfiesδ([[A,B],C])=[[6(A),B],C]+[[A,δ(B)],C]+[[A,B],δ(C)] fir all A,B,C∈AlgN. Thenδ=D+τ,where D is an additive derivation,τ:AlgN→CI satisfiesτ([A,B],C])= 0 for all A,B,C∈AlgN.2.Let N be a nlest on Hilbert space H.Suppose that the mapδ:AlgN→B(H) satisfiesδ(AB+BA)=δ(A)B+Aδ(B)+δ(B)A+Bδ(A) for all A,B∈AlgN. Thenδis an additive derivation.