Lie triple centralizers and generalized Lie triple derivations on triangular operator algebras by local actions

Let U be a triangular operator algebra, and ?: U ? U be a linear map. In this paper, under some mild conditions on U, we prove that if ? satisfies ?([[U, V], W ]) = [[?(U), V], W ] = [[U, ?(V)], W] for any U, V, W ? U with UV = UW = P being the standard idempotent(resp. UV = UW = 0), then there exist ? ? Z(U) and a linear map ?: U ? Z(U) satisfying ?([[U, V], W ]) = 0 for any U, V, W ? U with UV = UW = P(resp.UV = UW = 0) such that ?(U) = ?U + ?(U) for U ? U. As an application, we give a characterization of generalized Lie triple derivations on U .