2-local Lie triple isomorphisms of nest algebras

Let N be a nontrivial nest on a complex separable Hilbert space H with dimH > 2, and AlgN be the associated nest algebra. Suppose that d : AlgN ? AlgN is an additive surjective 2-local Lie triple isomorphism. If AlgN is not of infinite multiplicity, we prove that d is of the form d(x) = f(x) + t (x) for any x ? AlgN, where f is an isomorphism or the negative of an anti-isomorphism and t : AlgN ? CI is a linear map with t([[x, y], z]) = 0 for all x,y, z ? AlgN.