H-Toeplitz operators on the function spaces

In this paper, we study several classes of H -Toeplitz operators (defined below) on the Hardy space H 2 . In particular, we prove that, for φ ∈ L ∞ , the adjoint of H -Toeplitz operators is hyponormal. Next, we investigate several properties of H -Toeplitz operators on the weighted Bergman spaces. F...

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Bibliographic Details
Published in:Monatshefte für Mathematik 2024, Vol.205 (4), p.757-786
Main Authors: Kim, Sumin, Ko, Eungil, Lee, Ji Eun, Lee, Jongrak
Format: Article
Language:English
Subjects:
Function space
Mathematics
Mathematics and Statistics
Operators
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Summary:In this paper, we study several classes of H -Toeplitz operators (defined below) on the Hardy space H 2 . In particular, we prove that, for φ ∈ L ∞ , the adjoint of H -Toeplitz operators is hyponormal. Next, we investigate several properties of H -Toeplitz operators on the weighted Bergman spaces. Finally, we give necessary and sufficient conditions for H -Toeplitz operators to be contractive and expansive on the weighted Bergman spaces.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-024-01985-9