Factorizations of EP Banach space operators and EP Banach algebra elements

TL;DR

This paper generalizes known characterizations of EP matrices, Hilbert space operators, and $C^*$-algebra elements to Banach space operators and Banach algebra elements using various factorizations, introducing new results in these areas.

Contribution

It provides a unified framework for characterizing EP elements in Banach spaces and algebras, extending classical results and presenting novel findings.

Findings

Generalized characterizations of EP Banach space operators

Extended EP properties to Banach algebra elements

Introduced new results in the context of Banach spaces and algebras

Abstract

EP Banach space operators and EP Banach algebra elements are characterized using different kinds of factorizations. The results obtained generalize well-known characterizations of EP matrices, EP Hilbert space operators and EP $C^*$-algebra elements. Furthermore, new results that hold in these contexts are presented.