{
  "id": "1209.0055",
  "version": "v1",
  "published": "2012-09-01T04:41:23.000Z",
  "updated": "2012-09-01T04:41:23.000Z",
  "title": "A Note on The Mazur-Ulam Property of Almost-CL-spaces",
  "authors": [
    "Dongni Tan",
    "Rui Liu"
  ],
  "comment": "8 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We introduce the (T)-property, and prove that every Banach space with the (T)-property has the Mazur-Ulam property (briefly MUP). As its immediate applications, we obtain that almost-CL-spaces admitting a smooth point(specially, separable almost-CL-spaces) and a two-dimensional space whose unit sphere is a hexagon has the MUP. Furthermore, we discuss the stability of the spaces having the MUP by the $c_0$- and $\\ell_1$-sums, and show that the space $C(K,X)$ of the vector-valued continuous functions has the the MUP, where $X$ is a separable almost-CL-space and $K$ is a compact metric space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-01T04:41:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "46B20",
      "46A22"
    ],
    "keywords": [
      "mazur-ulam property",
      "compact metric space",
      "separable almost-cl-space",
      "immediate applications",
      "unit sphere"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.0055T"
    }
  }
}