Article
| Title: | The generalized Toeplitz operators on the Fock space $F_{\alpha }^{2}$ (English) |
| Author: | Xu, Chunxu |
| Author: | Yu, Tao |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 1 |
| Year: | 2024 |
| Pages: | 231-246 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $\mu $ be a positive Borel measure on the complex plane $\mathbb {C}^n$ and let $j=(j_1,\cdots ,j_n)$ with $j_i\in \mathbb {N}$. We study the generalized Toeplitz operators $T_{\mu }^{(j)}$ on the Fock space $F_{\alpha }^{2}$. We prove that $T_{\mu }^{(j)}$ is bounded (or compact) on $F_{\alpha }^{2}$ if and only if $\mu $ is a Fock-Carleson measure (or vanishing Fock-Carleson measure). Furthermore, we give a necessary and sufficient condition for $T_{\mu }^{(j)}$ to be in the Schatten $p$-class for $1\leq p<\infty $. (English) |
| Keyword: | generalized Toeplitz operator |
| Keyword: | boundedness |
| Keyword: | compactness |
| Keyword: | Schatten class |
| Keyword: | Fock space |
| MSC: | 30H20 |
| MSC: | 47B35 |
| idZBL: | Zbl 07893376 |
| idMR: | MR4717831 |
| DOI: | 10.21136/CMJ.2024.0066-23 |
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| Date available: | 2024-03-13T10:08:43Z |
| Last updated: | 2024-12-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152277 |
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