Characterizations of Lie centralizers of triangular algebras

Let A be an unital algebra over the complex field C. A linear map phi from A into itself is called a Lie centralizer at a given point G is an element of A if phi([S, T]) = [S, phi(T)] = [phi(S), T] for all S,T is an element of A with ST = G. The aim of this paper is to give a description of Lie centralizers at an arbitrary but fixed point on triangular algebras. These results are then applied to nest algebras and upper triangular matrix algebras.