{
  "id": "1204.2046",
  "version": "v1",
  "published": "2012-04-10T05:17:39.000Z",
  "updated": "2012-04-10T05:17:39.000Z",
  "title": "Orbits of linear operators and Banach space geometry",
  "authors": [
    "Jean-Matthieu Augé"
  ],
  "comment": "16 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $T$ be a bounded linear operator on a (real or complex) Banach space $X$. If $(a_n)$ is a sequence of non-negative numbers tending to 0. Then, the set of $x \\in X$ such that $\\|T^nx\\| \\geqslant a_n \\|T^n\\|$ for infinitely many $n$'s has a complement which is both $\\sigma$-porous and Haar-null. We also compute (for some classical Banach space) optimal exponents $q>0$, such that for every non nilpotent operator $T$, there exists $x \\in X$ such that $(\\|T^nx\\|/\\|T^n\\|) \\notin \\ell^{q}(\\mathbb{N})$, using techniques which involve the modulus of asymptotic uniform smoothness of $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-10T05:17:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A05",
      "47A16",
      "28A05"
    ],
    "keywords": [
      "banach space geometry",
      "non nilpotent operator",
      "asymptotic uniform smoothness",
      "bounded linear operator",
      "classical banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2046A"
    }
  }
}