# Compact operator semigroups applied to dynamical systems

## TL;DR

This paper develops a comprehensive theory of compact operator semigroups on locally convex spaces, extending mean ergodic theorems and applying them to various concepts in topological dynamics.

## Contribution

It introduces generalized mean ergodic theorems for compact operator semigroups on locally convex spaces, broadening the understanding of ergodic properties in topological dynamics.

## Key findings

- New generalized mean ergodic theorems established
- Application to different notions of mean ergodicity in topological dynamics
- Enhanced theoretical framework for compact operator semigroups

## Abstract

In this paper we develop a systematic theory of compact operator semigroups on locally convex vector spaces. In particular we prove new and generalized versions of the mean ergodic theorem and apply them to different notions of mean ergodicity appearing in topological dynamics.