On centralizers of prime rings with involution

‎Let $R$ be a ring with involution $*$‎. ‎An additive mapping $T:R\to R$ is called a left(respectively right) centralizer if $T(xy)=T(x)y$ (respectively $T(xy)=xT(y)$) for all $x,y\in R$‎. ‎The purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.