Let U be a 2-torsion free unital generalized matrix algebra, and φ : U → U be a linear map satisfying S, T ∈ U, ST = 0 ⇒ φ([S, T ]) = [φ(S), T ] = [S, φ(T )]. In this paper, we study the structure of φ and under some mild conditions on U we present the necessary and sufficient conditions for φ to be in terms of centralizers. We then provide the characterizations of Lie centralizers on U and our results generalize some of the previous results. We also refer to some applications of our results for triangular algebras and some operator algebras
