Generalized Jordan derivation on nest algebras

Let N be a nest on a Banach space X, and be the associated nest algebra. In this paper, we prove that, if there is a nontrivial element in N which is complemented in X, then every additive generalized Jordan derivation from into itself is an additive generalized derivation. Moreover, we give a characterization of linear generalized Jordan derivations of nest algebras on complex separable Hilbert spaces.