Weyl type theorems for hypercyclic, supercyclic, and Toeplitz operators

TL;DR

This paper investigates Weyl type theorems for hypercyclic, supercyclic, and Toeplitz operators, focusing on property $(UW_E)$, stability under perturbations, and providing examples on Bergman spaces.

Contribution

It introduces new results on the stability of Weyl type theorems for Toeplitz operators and explores property $(UW_E)$ for hypercyclic and supercyclic operators.

Findings

Property $(UW_E)$ studied for hypercyclic and supercyclic operators

Stability of Weyl type theorems under compact perturbations established for Toeplitz operators

Examples of Toeplitz operators satisfying Weyl type theorems provided on Bergman spaces

Abstract

In this paper, we study property $(UW_E)$ for hypercyclic and supercyclic operators. The stability of variants of Weyl type theorems under compact perturbations for Toeplitz operators on the Bergman space is also studied. We also provide some examples of Toeplitz operators satisfying Weyl type theorems on the Bergman space and the harmonic Bergman space.