Characterizations of Lie centralizers of triangular algebras.

Let A be an unital algebra over the complex field C . A linear map ϕ from A into itself is called a Lie centralizer at a given point G ∈ A if ϕ ([ S , T ]) = [ S , ϕ (T) ] = [ ϕ (S) , T ] for all S , T ∈ 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. [ABSTRACT FROM AUTHOR]