Lie derivable maps on nest algebras

Let \(\mathcal {N}\) $\mathcal{N}$ be a non-trivial nest on a Hilbert space H and \(\textrm{alg}\mathcal {N}\) $\text{alg}\mathcal{N}$ be the associated nest algebra. Let \(G\in \textrm{alg}\mathcal {N}\) $G\in \text{alg}\mathcal{N}$ be an operator with \(\overline{\textrm{ran}(G)}\in \mathcal {N}\backslash \{H\}\) $\overline{\text{ran}(G)}\in \mathcal{N}\backslash \{H\}$ . In this note, we give a description of Lie derivable maps and generalized Lie 2-derivable maps at G of nest algebra \(\textrm{alg}\mathcal {N}\) $\text{alg}\mathcal{N}$ .