Essential Descent Spectrum Equality

TL;DR

This paper investigates conditions under which the descent spectrum of a bounded operator on a Banach space equals its essential descent spectrum, contributing to the spectral theory of operators.

Contribution

It provides new conditions ensuring the equality of descent spectrum and essential descent spectrum for a single bounded operator.

Findings

Identifies specific conditions for spectrum equality

Establishes when descent spectrum coincides with essential descent spectrum

Enhances understanding of spectral properties of bounded operators

Abstract

A bounded operator $T$ in a Banach space $X$ is said to satisfy the essential descent spectrum equality, if the descent spectrum of $T$ as an operator on $X$ coincides with the essential descent spectrum of $T$. In this note, we give some conditions under which the equality $\sigma_{desc}(T) = \sigma^e_{desc}(T)$ holds for a single operator $T$.