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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: 2024-10-04
Stable URL: http://hdl.handle.net/10338.dmlcz/150621
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