{
  "id": "2301.08471",
  "version": "v1",
  "published": "2023-01-20T08:55:27.000Z",
  "updated": "2023-01-20T08:55:27.000Z",
  "title": "A geometric characterization of range-kernel complementarity",
  "authors": [
    "Dimosthenis Drivaliaris",
    "Nikos Yannakakis"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that a bounded linear operator on a Banach space with closed range has range-kernel complementarity if and only if its generalized amplitude is less than $\\pi$. An application to the strong convergence of the iterations of a bounded linear operator is also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-20T08:55:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A05",
      "47A10",
      "46C50"
    ],
    "keywords": [
      "range-kernel complementarity",
      "geometric characterization",
      "bounded linear operator",
      "banach space",
      "strong convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}