In this paper, we introduce the weighted generalized core-EP inverse in the context of a Banach *-algebra. We extend certain properties of the weighted core-EP inverse for rectangular complex matrices and bounded linear operators on Hilbert spaces, and we also establish some new properties. Furthermore, we present properties of the weighted generalized core-EP orders for all elements that are weighted g-Drazin invertible within a Banach *-algebra.
Chen et al. (Wed,) studied this question.