On the structure of some nonlinear maps in prime *-rings

Abstract

The objective of this paper is to introduce the notion of skew Lie centralizers in *-rings, and to investigate the structure of skew Lie centralizers and strong skew commutativity preserving maps in prime *-rings without assuming the existence of a symmetric idempotent and the unital element. As an application, we shall characterize such maps in different operator algebras.