Spectral equality for $C_0$ semigroups

TL;DR

This paper investigates conditions under which $C_0$ semigroups exhibit spectral equality for various spectra and establishes spectral inclusion results for B-Fredholm spectra, advancing the understanding of spectral properties in operator theory.

Contribution

It provides new conditions for spectral equality and inclusion for $C_0$ semigroups across different spectral types, extending existing spectral theory.

Findings

Spectral equality conditions for semiregular, essentially semiregular, and semi-Fredholm spectra.

Spectral inclusion results for B-Fredholm spectrum of $C_0$ semigroups.

Enhanced understanding of spectral behavior in operator semigroup theory.

Abstract

In this paper, we give conditions for which the $C_0$ semigroups satisfies spectral equality for semiregular, essentially semiregular and semi-Fredholm spectrum. Also, we establish the spectral inclusion for B-Fredholm spectrum of a $C_0$ semigroups.