{
  "id": "2401.13281",
  "version": "v1",
  "published": "2024-01-24T07:46:09.000Z",
  "updated": "2024-01-24T07:46:09.000Z",
  "title": "On the metric of the jet bundle and similarity on Dirichlet spaces",
  "authors": [
    "Kui Ji",
    "Shanshan Ji",
    "Hyun-Kyoung Kwon",
    "Xiaoceng Liu",
    "Jing Xu"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In general, it is more difficult to formulate a sufficient condition for similarity than a necessary condition. We give a sufficient condition for a Cowen-Douglas operator with a positivity condition to be similar to the backward shift operator on weighted Dirichlet space. This condition involves the holomorphic jet bundle of the eigenvector bundle of the operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-24T07:46:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "similarity",
      "sufficient condition",
      "holomorphic jet bundle",
      "necessary condition",
      "eigenvector bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}