{
  "id": "2407.17352",
  "version": "v1",
  "published": "2024-07-24T15:24:22.000Z",
  "updated": "2024-07-24T15:24:22.000Z",
  "title": "Invariant subspaces of perturbed backward shift",
  "authors": [
    "Soma Das",
    "Jaydeb Sarkar"
  ],
  "comment": "26 pages",
  "categories": [
    "math.FA",
    "math.CV",
    "math.OA"
  ],
  "abstract": "We represent closed subspaces of the Hardy space that are invariant under finite-rank perturbations of the backward shift. We apply this to classify almost invariant subspaces of the backward shift and represent closed subspaces that are invariant under a more refined version of nearly invariant subspaces of the backward shift. Kernels of certain perturbed Toeplitz operators are examples of the newly introduced nearly invariant subspaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-24T15:24:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30H10",
      "47A15",
      "47B35",
      "46E22"
    ],
    "keywords": [
      "invariant subspaces",
      "perturbed backward shift",
      "represent closed subspaces",
      "hardy space",
      "finite-rank perturbations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}