{
  "id": "1912.13266",
  "version": "v1",
  "published": "2019-12-31T11:06:22.000Z",
  "updated": "2019-12-31T11:06:22.000Z",
  "title": "Invertibility, Fredholmness and kernels of dual truncated Toeplitz operators",
  "authors": [
    "M. Cristina Câmara",
    "Kamila Kliś-Garlicka",
    "Bartosz Łanucha",
    "Marek Ptak"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Asymmetric dual truncated Toeplitz operators acting between the orthogonal complements of two (eventually different) model spaces are introduced and studied. They are shown to be equivalent after extension to paired operators on $L^2(\\mathbb T) \\oplus L^2(\\mathbb T)$ and, if their symbols are invertible in $L^\\infty(\\mathbb T)$, to asymmetric truncated Toeplitz operators with the inverse symbol. Relations with Carleson's corona theorem are also established. These results are used to study the Fredholmness, the invertibility and the spectra of various classes of dual truncated Toeplitz operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-31T11:06:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invertibility",
      "fredholmness",
      "truncated toeplitz operators acting",
      "asymmetric dual truncated toeplitz operators",
      "asymmetric truncated toeplitz operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}