Hyponormal dual Toeplitz operators on the orthogonal complement of the Harmonic Bergman space

2021/01/03 by Chongchao Wang, Wang, Chongchao, Xianfeng Zhao +1
Mathematics · #47B20 #47B32 #47B35 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2101.00552

openalex publication_date 2021/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space. First we show that the dual Toeplitz operator with bounded symbol is hyponormal if and only if it is normal. Then we obtain a necessary and sufficient condition for the dual Toeplitz operator S_φ with the symbol φ(z) = az^n₁z^m₁ + bz^n₂ z^m₂, (n₁,n₂,m₁,m₂∈ \mathbb N and a,b ∈ ℂ) to be hyponormal. Finally, we show that the rank of the commutator of two dual Toeplitz operators must be an even number if the commutator has a finite rank.

Related

• A New Necessary Condition for the Hyponormality of Toeplitz Operators on the Bergman Space
• Hyponormal Toeplitz Operators on Weighted Bergman Space
• Hyponormal block Toeplitz operators with non-harmonic symbols on the weighted Bergman space
• Which hyponormal block Toeplitz operators are either normal or analytic?
• The spectral picture of Bergman Toeplitz operators with harmonic polynomial symbols