Lie Triple Derivations of CSL Algebras

Let be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space with , and the associated CSL algebra. It is proved that every Lie triple derivation from into any sigma-weakly closed algebra containing is of the form X -> XT-TX+h(X)I, where and h is a linear mapping from into a, such that h([[A,B],C])=0 for all .