{
  "annotation_id": "749817d8-61c8-4df2-a9d6-3a737ab34618",
  "date_created": "2026-02-17T05:53:23.616000Z",
  "date_modified": "2026-02-17T05:53:23.616000Z",
  "file_hash": "806874143fdf0605436593ac8ac80011a98cc31be31bd90ff45fcf14f98f3505",
  "private": false,
  "record": {
    "abstract": "We study Toeplitz operators with measure-valued symbols acting between Fock spaces. Given $1\\le p,q\\le\\infty$ and a Borel measure $\\mu$ on $\\mathbb C$, we investigate when the associated Toeplitz operator \\[ T_\\mu : F^p_\\alpha \\to F^q_\\alpha \\] belongs to the nuclear class. For positive measures $\\mu$ and in the range $1\\le q\\le p\\le\\infty$, we obtain necessary and sufficient conditions for the nuclearity of $T_\\mu$ in terms of the Berezin transform of $\\mu$. As a consequence, nuclearity in this setting exhibits a rigidity property: if $T_\\mu$ is nuclear from $F^p_\\alpha$ to $F^q_\\alpha$ for some $q\\le p$, then it is nuclear for all such $q$. In the case $p\u003cq$, we show that the situation is more delicate. We provide separate necessary and sufficient conditions for nuclearity, indicating that the Berezin transform alone does not yield a complete characterization. The proofs rely on tools from Banach space operator theory combined with kernel estimates on Fock spaces. Our results extend naturally to Fock spaces on $\\mathbb C^n$.",
    "arxiv_id": "2601.10217",
    "authors": [
      "Tengfei Ma",
      "Yufeng Lu",
      "Chao Zu"
    ],
    "categories": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Nuclear Toeplitz operators between Fock spaces",
    "url": "https://arxiv.org/abs/2601.10217",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ee9bb1bc-3418-41b3-aa88-a2e24aaeab5d",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}