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Commutants of the sum of two quasihomogeneous Toeplitz operators
Bouhali, Aissa Louhichi, Issam
Bouhali, Aissa
Louhichi, Issam
Date
2024-03-12
Author
Advisor
Type
Article
Peer-Reviewed
Published version
Peer-Reviewed
Published version
Degree
Description
Abstract
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 𝑆 =𝑇𝑒𝑖𝑚𝜃𝑓 +𝑇𝑒𝑖𝑙𝜃𝑔 , where 𝑓 and 𝑔 are radial functions, commutes with a sum 𝑇 =𝑇𝑒𝑖𝑝𝜃𝑟(2𝑀+1)𝑝 +𝑇𝑒𝑖𝑠𝜃𝑟(2𝑁+1)𝑠 , then 𝑆 must be of the form 𝑆 =𝑐𝑇 , where 𝑐 is a constant. In this article, we will replace 𝑟(2𝑀+1)𝑝 and 𝑟(2𝑁+1)𝑠 with 𝑟𝑛 and 𝑟𝑑 , where 𝑛 and 𝑑 are in ℕ , and we will show that the same result holds.