{
  "id": "math/0604159",
  "version": "v1",
  "published": "2006-04-07T06:53:23.000Z",
  "updated": "2006-04-07T06:53:23.000Z",
  "title": "Occasionally attracting compact sets and compact-supercyclicity",
  "authors": [
    "K. Storozhuk"
  ],
  "comment": "5 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X$ be a real or complex Banach space and $T_t:X\\to X$ is a power bounded operator (or a $C_0$-semigroup). If there exists a \"occasionally\" attracting compact subset K (for each x$ in unit ball $\\liminf_n \\rho(T^n x, K)=0$ then there exists attracting finite-dimensional subspace $L$ (for each x in X $\\lim_n \\rho(T^n x, L)=0$. Also we define the compact-supercyclicity. Each infinity-dimentional $X$ has no compact-supercyclic isometries. If $T$ is a supercyclic and power bounded that $T^nx$ vanishes for each $x$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-07T06:53:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A60",
      "47A16"
    ],
    "keywords": [
      "occasionally attracting compact sets",
      "compact-supercyclicity",
      "complex banach space",
      "attracting compact subset",
      "power bounded operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4159S"
    }
  }
}