# Hypercyclicity and compactness of co-analytic Toeplitz operators on de Branges-Rovnyak spaces

## TL;DR

This paper investigates the conditions under which Toeplitz operators on de Branges-Rovnyak spaces are compact or hypercyclic, emphasizing the influence of the generating function b's properties.

## Contribution

It provides new characterizations of compactness and hypercyclicity of Toeplitz operators based on properties of the function b in de Branges-Rovnyak spaces.

## Key findings

- Compactness depends on whether b is an inner function.
- Hypercyclicity depends on the integrability of log(1-|b|).
- The function b's properties fundamentally influence operator behavior.

## Abstract

We study the compactness and the hypercyclicity of Toeplitz operators in the de Branges-Rovnyak spaces H(b) with co-analytic and bounded symbols on D. We highlight the fundamental role played by the function b generating the de Branges-Rovnyak space H(b). The characterization of compactness depends wether b is inner function or not and the characterization of hypercyclicity depends wether the function log(1-|b|) is integrable or not.