{
  "id": "0806.1815",
  "version": "v1",
  "published": "2008-06-11T08:51:44.000Z",
  "updated": "2008-06-11T08:51:44.000Z",
  "title": "Quotients of Banach spaces with the Daugavet property",
  "authors": [
    "Vladimir Kadets",
    "Varvara Shepelska",
    "Dirk Werner"
  ],
  "comment": "15 pages",
  "journal": "Bull. Pol. Acad. Sci. 56, no.2, 131-147 (2008)",
  "categories": [
    "math.FA"
  ],
  "abstract": "We consider a general concept of Daugavet property with respect to a norming subspace. This concept covers both the usual Daugavet property and its weak$^*$ analogue. We introduce and study analogues for narrow operators and rich subspaces in this general setting and apply the results to show that a quotient of $L_1[0,1]$ over an $\\ell_1$-subspace can fail the Daugavet property. The latter answers a question posed to us by A. Pelczynski in the negative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-11T08:51:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "46B25",
      "47B38"
    ],
    "keywords": [
      "banach spaces",
      "usual daugavet property",
      "study analogues",
      "concept covers",
      "general concept"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.1815K"
    }
  }
}