Lie triple derivations of nest algebras on Banach spaces

Let N be a non-trivial nest on X, AlgN be the associated nest algebra, and L:AlgN→B(X) be a linear mapping. In this paper, it is proved that L is a Lie triple derivation if and only if there exist a derivation d:AlgN→B(X) and a linear mapping h:AlgN→CI with h([[X,Y],Z])=0 for any X,Y,Z∈AlgN such that L=d+h on AlgN.