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

TL;DR

This paper explores the properties and characterizations of the Moore-Penrose inverse for EP operators and elements within Banach spaces and algebras, extending known Hilbert space results.

Contribution

It extends the theory of Moore-Penrose inverses and EP elements from Hilbert spaces and $C^*$-algebras to Banach spaces and algebras, providing new characterizations.

Findings

Characterization of EP Banach space operators

Extension of Hilbert space results to Banach algebras

New properties of Moore-Penrose inverse in Banach contexts

Abstract

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.