Work

Algebraic and spectral properties of H-Toeplitz operators on the Bergman space

Year: 2025

Type: article

Abstract: In this paper, we discuss the zero product problem of two H-Toeplitz operators and the commuting problem of H-Toeplitz and Hankel operators on the Bergman space. We establish necessary and sufficient conditions for the product of an H-Toeplitz operator and a Hankel operator equals another H-Toeplitz (Hankel) operator for a certain class of symbols. Moreover, we study the spectrum of the H-Toeplitz operators $ B_{z^{N}} $ and $ B_{\overline{z}^{N}} $, where $ N $ is a non-negative integer.

Source: AIMS Mathematics

DOI: 10.3934/math.2025603

Author: Jie Zhang

Institution: Chongqing University

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities