On the Moore–Penrose inverse, EP Banach space operators, and EP Banach algebra elements

The main concern of this note is the Moore–Penrose inverse in the context of Banach spaces and algebras. Especially attention will be given to a particular class of elements with the aforementioned inverse, namely EP Banach space operators and Banach algebra elements, which will be studied and characterized extending well-known results obtained in the frame of Hilbert space operators and C∗-algebra elements.