Characterizations of EP and normal Banach algebra elements and Banach space operators

TL;DR

This paper explores new characterizations of EP and normal elements in Banach algebras and extends known results from matrices and Hilbert space operators to a broader Banach space context.

Contribution

It introduces novel characterizations of EP and normal Moore-Penrose invertible elements in Banach algebras and extends classical results to Banach space operators.

Findings

Characterizations of EP elements in Banach algebras

Characterizations of normal Moore-Penrose invertible elements

Extension of matrix and Hilbert space results to Banach space operators

Abstract

Several characterizations of EP and normal Moore-Penrose invertible Banach algebra elements will be considered. The Banach space operator case will be also studied. The results of the present article will extend well known facts obtained in the frames of matrices and Hilbert space operators.