Hyponormal Toeplitz Operators on the Bergman Space of the Disk
| Autor: | Revilla, Nicole, Simanek, Brian |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We consider Toeplitz operators with bounded symbol acting on the Bergman space of the unit disk and assess their hyponormality. We will mainly be concerned with the symbol $\varphi(z)=z^{n}|z|^{2s}+a(t)\bar{z}^{m}|z|^{2t}$, where $s$ and $t$ are positive real numbers and $m$ and $n$ are natural numbers. The main goal is to understand how large $|a(t)|$ can be for this operator to be hyponormal and we will answer this question for large values of $t$. We also correct a typo from a 2019 paper of Fleeman and Liaw concerning the norm of the commutator of the Toeplitz operator with symbol $z^m\bar{z}^n$ when $m>n$. Comment: 11 pages, 1 figure |
| Databáze: | arXiv |
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