A note on Jordan left *-centralizers on prime and semiprime rings with involution

The aim of this note is to give alternative and short proofs for some results to Ali et al. in [3] by using the relationship between the concepts of Jordan left *-centralizer and right centralizer on a 2-torsion free semiprime rings endowed with involution. Keywords: Prime ring, Semiprime ring, Involution, Left (right) centralizer, Left (right) *-centralize