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 σ -weakly closed algebra containing is of the form X → XT − TX + h ( X ) I , where and h is a linear mapping from into ℂ such that h ([[ A , B ], C ])=0 for all .