{
  "id": "math/9412216",
  "version": "v1",
  "published": "1994-12-19T17:18:24.000Z",
  "updated": "1994-12-19T17:18:24.000Z",
  "title": "Extremal properties of contraction semigroups on $c_o$",
  "authors": [
    "P. K. Lin"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "For any complex Banach space $X$, let $J$ denote the duality mapping of $X$. For any unit vector $x$ in $X$ and any ($C_0$) contraction semigroup $(T_t)_{t>0}$ on $X$, Baillon and Guerre-Delabriere proved that if $X$ is a smooth reflexive Banach space and if there is $x^* \\in J(x)$ such that $|\\langle T(t) \\, x,J(x)\\rangle| \\to 1 $ as $t \\to \\infty$, then there is a unit vector $y\\in X$ which is an eigenvector of the generator $A$ of $(T_t)_{t>0}$ associated with a purely imaginary eigenvalue. They asked whether this result is still true if $X$ is replaced by $c_o$. In this article, we show the answer is negative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1994-12-19T17:18:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "contraction semigroup",
      "extremal properties",
      "unit vector",
      "complex banach space",
      "smooth reflexive banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1994math.....12216L"
    }
  }
}