Lie triple and Jordan derivable mappings on nest algebras

摘要

Let N be a nontrivial nest on a Banach space X over the complex field C, assume that there exists a nontrivial element in N which is complemented in X. Let Alg N be the associated nest algebra. In this article, we show that if δ is a Lie triple derivable mapping from Alg N into B(X) then for any A, B ∈ Alg N there exists a λ_(A,B) (depending on A and B) in C such that δ(A + B) = δ(A) + δ(B) + λ_(A,B)I, and δ = D + τ, where D is an additive derivation from Alg N into B(X) and τ is a mapping from Alg N into CI such that τ(A + B) = τ(A) + τ(B) + λA,BI and τ([[A, B], C]) = 0 for all A, B, C ∈ Alg N. We also show that if δ is a Jordan derivable mapping from Alg N into B(X) then δ is an additive derivation.