{
  "annotation_id": "4ca01f75-c178-4ec6-95c6-1dec34798e1f",
  "date_created": "2026-02-17T05:53:20.069000Z",
  "date_modified": "2026-02-17T05:53:20.069000Z",
  "file_hash": "79189e6c3d685369fd8673fb2bec287fea5e9cf76203f9cf0ad50cfbefb80090",
  "private": false,
  "record": {
    "abstract": "This paper studies the compressed shift operator $S_z$ on the Hardy space over the bidisk via the geometric approach. We calculate the spectrum and essential spectrum of $S_z$ on the Beurling type quotient modules induced by rational inner functions, and give a complete characterization for $S_z^*$ to be a Cowen-Douglas operator. Then we extend the concept of Cowen-Douglas operator to be the generalized Cowen-Douglas operator, and show that $S_z^*$ is a generalized Cowen-Douglas operator. Moreover, we establish the connection between the reducibility of the Hermitian holomorphic vector bundle induced by kernel spaces and the reducibility of the generalized Cowen-Douglas operator. By using the geometric approach, we study the reducing subspaces of $S_z$ on certain polynomial quotient modules.",
    "arxiv_id": "2601.09145",
    "authors": [
      "Yufeng Lu",
      "Yixin Yang",
      "Chao Zu"
    ],
    "categories": [
      "math.FA",
      "math.CV"
    ],
    "doi": "10.1016/j.jfa.2023.110063",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "A geometric approach to the compressed shift operator on the Hardy space over the bidisk",
    "url": "https://arxiv.org/abs/2601.09145",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c7172535-78fa-4008-9b4f-1673a52b25bd",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}