Generalized weighted EP elements in Banach algebras

We propose a new class of generalized inverses with weights, which represent a natural extension of EP (Moore-Penrose) and *-DMP (Drazin-Moore-Penrose) elements in a Banach *-algebra. This paper presents various characteristics of weighted EP elements. Moreover, we characterize the weighted EP element through the core-EP decomposition and a polar-like property. Finally, we explore weighted *-DMP elements and uncover several new properties of *-DMP elements.