{
  "id": "2005.02255",
  "version": "v1",
  "published": "2020-05-05T14:51:34.000Z",
  "updated": "2020-05-05T14:51:34.000Z",
  "title": "Kernels of Perturbed Toeplitz Operators in vector-valued Hardy spaces",
  "authors": [
    "Arup Chattopadhyay",
    "Soma Das",
    "Chandan Pradhan"
  ],
  "comment": "28 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Recently, Liang and Partington \\cite{YP} show that kernels of finite-rank perturbations of Toeplitz operators are nearly invariant with finite defect under the backward shift operator acting on the scalar-valued Hardy space. In this article we provide a vectorial generalization of a result of Liang and Partington. As an immediate application we identify the kernel of perturbed Toeplitz operator in terms of backward shift-invariant subspaces in various important cases by applying the recent theorem (\\cite{CDP, OR}) in connection with nearly invariant subspaces of finite defect for the backward shift operator acting on the vector-valued Hardy space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-05T14:51:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A13",
      "47A15",
      "47A80",
      "46E20",
      "47B38",
      "47B32",
      "30H10"
    ],
    "keywords": [
      "perturbed toeplitz operator",
      "vector-valued hardy space",
      "backward shift operator acting",
      "finite defect",
      "shift-invariant subspaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}