{
  "id": "1612.02025",
  "version": "v1",
  "published": "2016-12-06T21:18:21.000Z",
  "updated": "2016-12-06T21:18:21.000Z",
  "title": "Lipschitz Embeddings of Metric Spaces into $c_0$",
  "authors": [
    "Florent P. Baudier",
    "Robert Deville"
  ],
  "comment": "14 pages, to appear in the Proceedings of the Conference on Harmonic and Functional Analysis, Operator Theory and Applications in honor of Jean Esterle",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "Let $M$ be a separable metric space. We say that $f=(f_n):M\\to c_0$ is a good-$\\lambda$-embedding if, whenever $x,y\\in M$, $x\\ne y$ implies $d(x,y)\\le\\Vert f(x)-f(y)\\Vert$ and, for each $n$, $Lip(f_n)<\\lambda$, where $Lip(f_n)$ denotes the Lipschitz constant of $f_n$. We prove that there exists a good-$\\lambda$-embedding from $M$ into $c_0$ if and only if $M$ satisfies an internal property called $\\pi(\\lambda)$. As a consequence, we obtain that for any separable metric space $M$, there exists a good-$2$-embedding from $M$ into $c_0$. These statements slightly extend former results obtained by N. Kalton and G. Lancien, with simplified proofs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-06T21:18:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46T99"
    ],
    "keywords": [
      "lipschitz embeddings",
      "separable metric space",
      "lipschitz constant",
      "internal property",
      "statements slightly extend"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}