Nuclear Toeplitz operators between Fock spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910045711630336 |
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| author | Ma, Tengfei Lu, Yufeng Zu, Chao |
| author_facet | Ma, Tengfei Lu, Yufeng Zu, Chao |
| contents | We characterize the nuclearity of Toeplitz operators $T_μ: F_α^p \to F_α^q$ with Borel measure symbols for $1\leq p,q\leq \infty$. For positive measures $μ$ and $q\leq p$, we provide necessary and sufficient conditions in terms of the Berezin transform and establish a rigidity property for nuclearity across this range. In the case $p<q$, we obtain separate necessary and sufficient conditions, indicating that the Berezin transform alone is insufficient for a complete characterization. Our results extend to Fock spaces on $\mathbb{C}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10217 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nuclear Toeplitz operators between Fock spaces Ma, Tengfei Lu, Yufeng Zu, Chao Functional Analysis Primary 47B10 Secondary 47B35 We characterize the nuclearity of Toeplitz operators $T_μ: F_α^p \to F_α^q$ with Borel measure symbols for $1\leq p,q\leq \infty$. For positive measures $μ$ and $q\leq p$, we provide necessary and sufficient conditions in terms of the Berezin transform and establish a rigidity property for nuclearity across this range. In the case $p<q$, we obtain separate necessary and sufficient conditions, indicating that the Berezin transform alone is insufficient for a complete characterization. Our results extend to Fock spaces on $\mathbb{C}^n$. |
| title | Nuclear Toeplitz operators between Fock spaces |
| topic | Functional Analysis Primary 47B10 Secondary 47B35 |
| url | https://arxiv.org/abs/2601.10217 |