{
  "id": "math/9406210",
  "version": "v1",
  "published": "1994-06-06T17:36:22.000Z",
  "updated": "1994-06-06T17:36:22.000Z",
  "title": "A remark on contraction semigroups on Banach spaces",
  "authors": [
    "P. K. Lin"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X$ be a complex Banach space and let $J:X \\to X^*$ be a duality section on $X$ (i.e. $\\langle x,J(x)\\rangle=\\|J(x)\\|\\|x\\|=\\|J(x)\\|^2=\\|x\\|^2$). For any unit vector $x$ and any ($C_0$) contraction semigroup $T=\\{e^{tA}:t \\geq 0\\}$, Goldstein proved that if $X$ is a Hilbert space and if $|\\langle T(t) x,J(x)\\rangle| \\to 1 $ as $t \\to \\infty$, then $x$ is an eigenvector of $A$ corresponding to a purely imaginary eigenvalue. In this article, we prove the similar result holds if $X$ is a strictly convex complex Banach space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1994-06-06T17:36:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "contraction semigroup",
      "strictly convex complex banach space",
      "similar result holds",
      "unit vector",
      "hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1994math......6210L"
    }
  }
}