| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2022-08-22T08:25:10Z |
| Last updated:
|
2024-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150621 |
| . |
| Reference:
|
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