Lie triple centralizers on generalized matrix algebras
Abstract
In this article, we introduce the notion of Lie triple centralizer as follows. Let (Figure presented.) be an algebra, and (Figure presented.) be a linear mapping. We say that ϕ is a Lie triple centralizer whenever (Figure presented.) for all (Figure presented.). Then we characterize the general form of Lie triple centralizers on a generalized matrix algebra (Figure presented.) and under some mild conditions on (Figure presented.) we present the necessary and sufficient conditions for a Lie triple centralizer to be proper. As an application of our results, we characterize generalized Lie triple derivations on generalized matrix algebras.