Absolutely Summing Toeplitz operators on Fock spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916967442546688 |
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| author | Hu, Zhangjian Wang, Ermin |
| author_facet | Hu, Zhangjian Wang, Ermin |
| contents | For $1\le p<\infty$, let $F^p_φ$ be the Fock spaces on ${\mathbb C}^n$ with the weight function $φ$ that \(φ\in {\mathcal{C}}^{2}\left( {\mathbb{C}}^{n}\right)\) is real-valued and satisfies
$
m{ω}_{0} \leq d{d}^{c}φ\leq M{ω}_{0}
$
for two positive constants \(m\) and \(M\), \({ω}_{0} = d{d}^{c}{\left| z\right| }^{2}\) is the Euclidean Kähler form on \({\mathbb{C}}^{n}\), \({d}^{c} = \frac{\sqrt{-1}}{4}\left( {\bar{\partial } - \partial }\right)\). In this paper, we completely characterize those positive Borel measure $μ$ on ${\mathbb C}^n$ so that the induced Toeplitz operators $T_μ$ is $r$-summing on $F_φ^{p}$ for $r \ge 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19967 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Absolutely Summing Toeplitz operators on Fock spaces Hu, Zhangjian Wang, Ermin Functional Analysis Complex Variables For $1\le p<\infty$, let $F^p_φ$ be the Fock spaces on ${\mathbb C}^n$ with the weight function $φ$ that \(φ\in {\mathcal{C}}^{2}\left( {\mathbb{C}}^{n}\right)\) is real-valued and satisfies $ m{ω}_{0} \leq d{d}^{c}φ\leq M{ω}_{0} $ for two positive constants \(m\) and \(M\), \({ω}_{0} = d{d}^{c}{\left| z\right| }^{2}\) is the Euclidean Kähler form on \({\mathbb{C}}^{n}\), \({d}^{c} = \frac{\sqrt{-1}}{4}\left( {\bar{\partial } - \partial }\right)\). In this paper, we completely characterize those positive Borel measure $μ$ on ${\mathbb C}^n$ so that the induced Toeplitz operators $T_μ$ is $r$-summing on $F_φ^{p}$ for $r \ge 1$. |
| title | Absolutely Summing Toeplitz operators on Fock spaces |
| topic | Functional Analysis Complex Variables |
| url | https://arxiv.org/abs/2509.19967 |