# Semi-Fredholm and Semi-Browder Spectra For $C_0$-Quasi-Semigroups

## TL;DR

This paper investigates various spectral properties of $C_0$-quasi-semigroups, linking their spectra to those of their generators, with a focus on essential ascent, descent, and semi-Fredholm and semi-Browder spectra.

## Contribution

It provides a detailed description of the spectra of $C_0$-quasi-semigroups in relation to their generators, including semi-Fredholm and semi-Browder spectra, which was not previously fully characterized.

## Key findings

- Spectral descriptions of $C_0$-quasi-semigroups in terms of their generators.
- Characterization of essential ascent and descent spectra.
- Analysis of Drazin invertibility and semi-Fredholm spectra.

## Abstract

In this paper, we describe the different spectra of the $C_0$-quasi-semigroups by the spectra of their generators. Specially, essential ascent and descent,Drazin invertible, upper and lower semi-Fredholm and semi-Browder spectra.