Lie triple derivations of nest algebras

Abstract

Let N be a nest on a complex separable Hilbert space H , and τ ( N ) be the associated nest algebra. In this paper, we prove that every Lie triple derivation from τ ( N ) into itself is of the form X → XT − TX + h( X) I, where T ∈ τ ( N ) and h is a linear mapping from τ ( N ) into C such that h([[ A, B], C]) = 0 for all A , B , C ∈ τ ( N ) .