{
  "id": "2210.04752",
  "version": "v1",
  "published": "2022-10-10T15:07:04.000Z",
  "updated": "2022-10-10T15:07:04.000Z",
  "title": "A note on the Krylov solvability of compact normal operators on Hilbert space",
  "authors": [
    "Noe Angelo Caruso"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We analyse the Krylov solvability of inverse linear problems on Hilbert space $\\mathcal{H}$ where the underlying operator is compact and normal. Our results explicitly describe the Krylov subspace for such operators given any datum vector $g\\in\\mathcal{H}$, as well as prove that all inverse linear problems are Krylov solvable provided that $g$ is in the range of the operator. We close the study by proving an isomorphism between the closed Krylov subspace for a general bounded normal operator and an $L^2$-measure space based on the scalar spectral measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-10T15:07:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact normal operators",
      "krylov solvability",
      "hilbert space",
      "inverse linear problems",
      "krylov subspace"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}