LIE CENTRALIZERS AND GENERALIZED LIE DERIVATIONS AT ZERO PRODUCTS

Abstract

Let $\mathcal{ℛ}$ be a unital prime ring with characteristic not $2$ and containing a nontrivial idempotent. We characterize Lie centralizers and generalized Lie derivations at zero products on $\mathcal{ℛ}$. The Lie centralizers and generalized Lie derivations on $\mathcal{ℛ}$ will be described. The obtained results are applied to Banach space standard operator algebras and factor von Neumann algebras.