Article
| Title: | Complex symmetry of Toeplitz operators on the weighted Bergman spaces (English) |
| Author: | Hu, Xiao-He |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 72 |
| Issue: | 3 |
| Year: | 2022 |
| Pages: | 855-873 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We give a concrete description of complex symmetric monomial Toeplitz operators $T_{z^p \bar {z}^q}$ on the weighted Bergman space $A^2(\Omega )$, where $\Omega $ denotes the unit ball or the unit polydisk. We provide a necessary condition for $T_{z^p \bar {z}^q}$ to be complex symmetric. When $p,q \in \mathbb {N}^2$, we prove that $T_{z^p \bar {z}^q}$ is complex symmetric on $A^2(\Omega )$ if and only if $p_1 = q_2$ and $p_2 = q_1$. Moreover, we completely characterize when monomial Toeplitz operators $T_{z^p \bar {z}^q}$ on $A^2(\mathbb {D}_{n})$ are $J_U$-symmetric with the $ n \times n$ symmetric unitary matrix $U$. (English) |
| Keyword: | complex symmetry |
| Keyword: | Toeplitz operator |
| Keyword: | weighted Bergman space |
| MSC: | 32A36 |
| MSC: | 47B35 |
| idZBL: | Zbl 07584106 |
| idMR: | MR4467946 |
| DOI: | 10.21136/CMJ.2022.0210-21 |
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| Date available: | 2022-08-22T08:25:10Z |
| Last updated: | 2022-12-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/150621 |
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