Resumen de The w -core–EP inverse in rings with involution

Dijana Mosic, Huihui Zhu, Liyun Hu

• The main goal of this paper is to present two new classes of generalized inverses in order to extend the concepts of the (dual) core–EP inverse and the (dual) w-core inverse. Precisely, we introduce the w-core–EP inverse and its dual for elements of a ring with involution. We characterize the (dual) w-core–EP invertible elements and develop several representations of the w-core–EP inverse and its dual in terms of different well-known generalized inverses. Using these results, we get new characterizations and expressions for the core–EP inverse and its dual. We apply the dual w-core–EP inverse to solve certain operator equations and give their general solution forms.