{
  "id": "2005.12786",
  "version": "v1",
  "published": "2020-05-26T15:09:17.000Z",
  "updated": "2020-05-26T15:09:17.000Z",
  "title": "Study of nearly invariant subspaces with finite defect in Hilbert spaces",
  "authors": [
    "Arup Chattopadhyay",
    "Soma Das"
  ],
  "comment": "22 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this article, we briefly describe nearly $T^{-1}$ invariant subspaces with finite defect for a shift operator $T$ having finite multiplicity acting on a separable Hilbert space $\\mathcal{H}$ as a generalization of nearly $T^{-1}$ invariant subspaces introduced by Liang and Partington in \\cite{YP}. In other words we characterize nearly $T^{-1}$ invariant subspaces with finite defect in terms of backward shift invariant subspaces in vector-valued Hardy spaces by using Theorem 3.5 in \\cite{CDP}. Furthermore, we also provide a concrete representation of the nearly $T_B^{-1}$ invariant subspaces with finite defect in a scale of Dirichlet-type spaces $\\mathcal{D}_\\alpha$ for $\\alpha \\in [-1,1]$ corresponding to any finite Blashcke product $B$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-26T15:09:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A13",
      "47A15",
      "47A80",
      "46E20",
      "47B38",
      "47B32",
      "30H10"
    ],
    "keywords": [
      "finite defect",
      "backward shift invariant subspaces",
      "finite blashcke product",
      "separable hilbert space",
      "finite multiplicity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}