{
  "id": "2005.14561",
  "version": "v1",
  "published": "2020-05-29T13:22:39.000Z",
  "updated": "2020-05-29T13:22:39.000Z",
  "title": "A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: Fredholm properties",
  "authors": [
    "G. J. Groenewald",
    "S. ter Horst",
    "J. Jaftha",
    "A. C. M. Ran"
  ],
  "comment": "25 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper concerns the analysis of an unbounded Toeplitz-like operator generated by a rational matrix function having poles on the unit circle T. It extends the analysis of such operators generated by scalar rational functions with poles on T found in [11,12,13]. A Wiener-Hopf type factorization of rational matrix functions with poles and zeroes on T is proved and then used to analyze the Fredholm properties of such Toeplitz-like operators. A formula for the index, based on the factorization, is given. Furthermore, it is shown that the determinant of the matrix function having no zeroes on T is not sufficient for the Toeplitz-like operator to be Fredholm, in contrast to the classical case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-29T13:22:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B35",
      "47A53",
      "47A68"
    ],
    "keywords": [
      "toeplitz-like operator",
      "rational matrix symbol",
      "fredholm properties",
      "unit circle",
      "rational matrix function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}