{
  "id": "2002.09167",
  "version": "v1",
  "published": "2020-02-21T07:45:16.000Z",
  "updated": "2020-02-21T07:45:16.000Z",
  "title": "Hyperinvariant subspace for absolutely norm attaining and absolutely minimum attaining operators",
  "authors": [
    "Neeru Bala",
    "Golla Ramesh"
  ],
  "comment": "submiited to a journal. Comments/suggestions are welcome",
  "categories": [
    "math.FA"
  ],
  "abstract": "A bounded linear operator $T:H_1\\rightarrow H_2$, where $H_1,\\,H_2$ are Hilbert spaces, is called \\textit{norm attaining} if there exist $x\\in H_1$ with unit norm such that $\\|Tx\\|=\\|T\\|$. If for every closed subspace $M\\subseteq H_1$, the operator $T|_M:M\\rightarrow H_2$ is norm attaining, then $T$ is called \\textit{absolutely norm attaining}. If in the above definitions $\\|T\\|$ is replaced by the minimum modulus, $m(T):=\\inf\\{\\|Tx\\|:x\\in H_1,\\|x\\|=1\\}$, then $T$ is called \\textit{minimum attaining} and \\textit{absolutely minimum attaining}, respectively. In this article, we show the existence of a non-trivial hyperinvariant subspace for absolutely norm (minimum) attaining normaloid (minimaloid) operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-21T07:45:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "47A15",
      "47A53",
      "47B07"
    ],
    "keywords": [
      "absolutely minimum attaining operators",
      "absolutely norm attaining",
      "non-trivial hyperinvariant subspace",
      "bounded linear operator",
      "minimum modulus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}