Characterizations of Lie centralizers of triangular algebras

Abstract

Let be an unital algebra over the complex field . A linear map ϕ from into itself is called a Lie centralizer at a given point if for all 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.