On the structure of some nonlinear maps in prime $\ast$-rings

Abstract

The objective of this manuscript 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 symmetric idempotent and the unital element. As an application we shall characterize such maps in different operator algebras.