Lie centralizers at the zero products on generalized matrix algebras

Abstract

Let [Formula: see text] be a 2-torsion free unital generalized matrix algebra, and [Formula: see text] be a linear map satisfying [Formula: see text] In this paper, we study the structure of [Formula: see text] and under some mild conditions on [Formula: see text] we present the necessary and sufficient conditions for [Formula: see text] to be in terms of centralizers. We then provide the characterizations of Lie centralizers on [Formula: see text] 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.