{
  "id": "math/0201144",
  "version": "v1",
  "published": "2002-01-16T14:00:18.000Z",
  "updated": "2002-01-16T14:00:18.000Z",
  "title": "Lipschitz spaces and M-ideals",
  "authors": [
    "Heiko Berninger",
    "Dirk Werner"
  ],
  "comment": "Includes 4 figures",
  "journal": "Extracta Math. 18, no.1, 33-56 (2003)",
  "categories": [
    "math.FA"
  ],
  "abstract": "For a metric space $(K,d)$ the Banach space $\\Lip(K)$ consists of all scalar-valued bounded Lipschitz functions on $K$ with the norm $\\|f\\|_{L}=\\max(\\|f\\|_{\\infty},L(f))$, where $L(f)$ is the Lipschitz constant of $f$. The closed subspace $\\lip(K)$ of $\\Lip(K)$ contains all elements of $\\Lip(K)$ satisfying the $\\lip$-condition $\\lim_{0<d(x,y)\\to 0}|f(x)-f(y)|/d(x,y)=0$. For $K=([0,1],| {\\cdot} |^{\\alpha})$, $0<\\alpha<1$, we prove that $\\lip(K)$ is a proper $M$-ideal in a certain subspace of $\\Lip(K)$ containing a copy of $\\ell^{\\infty}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-01-16T14:00:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "46B20",
      "46E15"
    ],
    "keywords": [
      "lipschitz spaces",
      "metric space",
      "lipschitz constant",
      "banach space",
      "scalar-valued bounded lipschitz functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1144B"
    }
  }
}