Drazin spectra of Banach space operators and Banach algebra elements

TL;DR

This paper investigates the relationships between the Drazin spectra of elements in Banach algebras and operators, providing new characterizations and extending results to Banach space operators.

Contribution

It introduces new relations and characterizations of the Drazin spectrum for Banach algebra elements and operators, enhancing understanding of spectral properties.

Findings

Relations among Drazin spectra of algebra elements and multiplication operators

Characterization of the Drazin spectrum in Banach algebras

Extension of spectral results to Banach space operators

Abstract

Given a Banach Algebra $A$ and $a\in A$, several relations among the Drazin spectrum of $a$ and the Drazin spectra of the multiplication operators $L_a$ and $R_a$ will be stated. The Banach space operator case will be also examined. Furthermore, a characterization of the Drazin spectrum will be considered.