Commutants of the sum of two quasihomogeneous Toeplitz operators

A major open question in the theory of Toeplitz operator on the Bergman space of the unit disk of the complex plane is the complete characterization of the set of all Toeplitz operators that commute with a given operator. Researchers showed that when a sum =⁢⁢⁢ +⁢⁢⁢ , where and are radial functions,...

Full description

Saved in:
Bibliographic Details
Main Author: Bouhali, Aissa (author)
Other Authors: Louhichi, Issam (author)
Format: article
Published: 2024
Subjects:
Online Access:https://hdl.handle.net/11073/33273
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A major open question in the theory of Toeplitz operator on the Bergman space of the unit disk of the complex plane is the complete characterization of the set of all Toeplitz operators that commute with a given operator. Researchers showed that when a sum =⁢⁢⁢ +⁢⁢⁢ , where and are radial functions, commutes with a sum =⁢⁢⁢(2⁢+1)⁢ +⁢⁢⁢(2⁢+1)⁢ , then must be of the form =⁢ , where is a constant. In this article, we will replace (2⁢+1)⁢ and (2⁢+1)⁢ with and , where and are in ℕ , and we will show that the same result holds.