In this article, we consider several local conditions under which linear mappings on algebras act like Lie n-centralizers and we study these linear mappings, Lie n-centralizers and n-commuting linear maps. With various examples, we compare Lie n-centralizers, n-commuting linear maps, and linear mappings acting similarly to Lie n-centralizers under different local conditions. In the following, we consider the mentioned concepts for linear mappings on standard operator algebras over a complex Banach space X with dimX ≥ 2. As an application of the obtained results, we present some variants of Posner’s second theorem on unital standard operator algebras.
