Abstract
In this paper, we give a characterization of normality of Toeplitz operator Tφ on the Bergman space A2(D). First, we state basic properties for Toeplitz operator Tφ on A2(D). Next, we consider the normal Toeplitz operator Tφ on A2(D) in terms of harmonic symbols φ. Finally, we characterize the normal Toeplitz operators Tφ with non-harmonic symbols acting on A2(D).
Highlights
The purpose of this paper is to study the normality of Toeplitz operators acting on the Bergman space
Our interest is focused on Toeplitz operators with harmonic and non-harmonic symbols
Halmos [7] characterized normal Toeplitz operators on the Hardy space. This contains many of the fundamental results on the algebraic properties of Toeplitz operators
Summary
The purpose of this paper is to study the normality of Toeplitz operators acting on the Bergman space. For f ∈ A2 (D) and P denotes the orthogonal projection of L2 (D) onto A2 (D) In this case, the function φ is called the symbol of Tφ. We will consider the normality of Toeplitz operators on the Bergman space with various symbols. Halmos [7] characterized normal Toeplitz operators on the Hardy space This contains many of the fundamental results on the algebraic properties of Toeplitz operators. The authors in [3] gave a properties of Tφ with non-harmonic symbols on the Bergman space. We characterize the normal Toeplitz operators Tφ with non-harmonic symbols acting on A2 (D).
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