Nuclear Toeplitz operators between Fock spaces

Tengfei Ma; Yufeng Lu; Chao Zu

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arXiv · 2601.10217

Nuclear Toeplitz operators between Fock spaces

Tengfei Ma·Yufeng Lu·Chao Zu

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Abstract

We characterize the nuclearity of Toeplitz operators $T_\mu: F_\alpha^p \to F_\alpha^q$ with Borel measure symbols for $1\leq p,q\leq \infty$. For positive measures $\mu$ 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 $\mathbb{C}^n$.

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BibTeX RIS

Tengfei Ma, Yufeng Lu, Chao Zu. 2026-01-15. Nuclear Toeplitz operators between Fock spaces. https://arxiv.org/abs/2601.10217

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