# The Ces\`aro operator on duals of smooth sequence spaces of infinite type

## TL;DR

This paper studies the spectral properties of the Cesàro operator on duals of smooth sequence spaces of infinite type, revealing significant differences based on nuclearity.

## Contribution

It provides a detailed spectral analysis of the Cesàro operator on these dual spaces, highlighting the impact of nuclearity on the spectrum.

## Key findings

- Spectrum differs markedly between nuclear and non-nuclear cases
- Identifies conditions under which the spectrum exhibits specific properties
- Advances understanding of operators on infinite-dimensional sequence spaces

## Abstract

The discrete Ces\`aro operator $\mathsf{C}$ is investigated in strong duals of smooth sequence spaces of infinite type. Of main interest is its spectrum, which turns out to be distinctly different in the cases when the space is nuclear and when it is not.