{
  "id": "1908.03555",
  "version": "v1",
  "published": "2019-08-09T17:53:17.000Z",
  "updated": "2019-08-09T17:53:17.000Z",
  "title": "The angle along a curve and range-kernel complementarity",
  "authors": [
    "Dimosthenis Drivaliaris",
    "Nikos Yannakakis"
  ],
  "categories": [
    "math.FA",
    "math.SP"
  ],
  "abstract": "In this paper, we define the angle of a bounded linear operator $A$ along an unbounded path emanating from the origin and use it to characterize range-kernel complementarity. In particular we show that if $0$ faces the unbounded component of the resolvent set, then $X=R(A)\\oplus N(A)$ if and only if $R(A)$ is closed and some angle of $A$ is less than $\\pi$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-09T17:53:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "47A15"
    ],
    "keywords": [
      "bounded linear operator",
      "characterize range-kernel complementarity",
      "resolvent set",
      "unbounded path",
      "unbounded component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}