Lie triple centralizers on generalized matrix algebras

Abstract

In this article, we introduce the notion of Lie triple centralizer as follows. Let A be an algebra, and ϕ : A → A be a linear mapping. We say that ϕ is a Lie triple centralizer whenever ϕ([[a, b], c]) = [[ϕ(a), b], c] for all a, b, c ∈ A. Then we characterize the general form of Lie triple centralizers on a generalized  matrix algebra U and under some mild conditions on U 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.