{
  "id": "1311.4429",
  "version": "v1",
  "published": "2013-11-18T15:54:56.000Z",
  "updated": "2013-11-18T15:54:56.000Z",
  "title": "Geometric characterization of $L_1$-spaces",
  "authors": [
    "Normuxammad Yadgorov",
    "Mukhtar Ibragimov",
    "Karimbergen Kudaybergenov"
  ],
  "comment": "Accepted to publication in the journal Studia Mathematica. arXiv admin note: text overlap with arXiv:math/0305342 by other authors",
  "journal": "Studia Mathematica 219 (2) 2013, 98-107",
  "doi": "10.4064/sm219-2-1",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "The paper is devoted to a description of all strongly facially symmetric spaces which are isometrically isomorphic to $L_1$-spaces. We prove that if $Z$ is a real neutral strongly facially symmetric space such that every maximal geometric tripotent from the dual space of $Z$ is unitary then, the space $Z$ is isometrically isomorphic to the space $L_1(\\Omega, \\Sigma, \\mu),$ where $(\\Omega, \\Sigma, \\mu)$ is an appropriate measure space having the direct sum property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-18T15:54:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20"
    ],
    "keywords": [
      "geometric characterization",
      "direct sum property",
      "real neutral strongly facially symmetric",
      "neutral strongly facially symmetric space",
      "appropriate measure space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.4429Y"
    }
  }
}