An Equation Related To Jordan *-Centralizers

Abstract

     Let R be a *-ring, an additive mapping T: R →R is called A left (right) Jordan *-centralizer of a *-ring R if satisfies T(x²)=T(x) x* (T(x²)= x*T(x)) for all x ÃŽ R. A Jordan *-centralizer of R is an additive mapping which is both left and right Jordan *-centralizer. The purpose of this paper is to prove the result concerning Jordan *-centralizer. The result which we refer state as follows: Let R be a 2-torsion free semiprime *-ring and let T: R ® R be an additive mapping such that 2T(x²) = T(x) x* + x* T(x) holds for all x ÃŽ R. In this case, T is a Jordan *-centralizer