Absolutely summing Hankel operators on Fock spaces and the Berger-Coburn phenomenon
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909980950528000 |
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| author | Hu, Zhangjian Lv, Xiaofen |
| author_facet | Hu, Zhangjian Lv, Xiaofen |
| contents | In this paper, for $1 \leq p, r < \infty$ we characterize those symbols $f$ so that the induced Hankel operators $H_f$ are $r$-summing from Fock spaces $F^p_α$ to $L^p_α$. The main result shows that the $r$-summing norm of $H_f$ is equivalent to the $\mathrm{IDA}^{κ, p}$-norm of $f$, where $κ$ is a positive number determined by $p$ and $r$, and the $\mathrm{IDA}$ space is as in [13]. As some application, we discuss the Berger-Coburn phenomenon for $r$-summing Hankel operators on Fock spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_01197 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Absolutely summing Hankel operators on Fock spaces and the Berger-Coburn phenomenon Hu, Zhangjian Lv, Xiaofen Functional Analysis Complex Variables In this paper, for $1 \leq p, r < \infty$ we characterize those symbols $f$ so that the induced Hankel operators $H_f$ are $r$-summing from Fock spaces $F^p_α$ to $L^p_α$. The main result shows that the $r$-summing norm of $H_f$ is equivalent to the $\mathrm{IDA}^{κ, p}$-norm of $f$, where $κ$ is a positive number determined by $p$ and $r$, and the $\mathrm{IDA}$ space is as in [13]. As some application, we discuss the Berger-Coburn phenomenon for $r$-summing Hankel operators on Fock spaces. |
| title | Absolutely summing Hankel operators on Fock spaces and the Berger-Coburn phenomenon |
| topic | Functional Analysis Complex Variables |
| url | https://arxiv.org/abs/2601.01197 |