{
  "id": "1111.6444",
  "version": "v1",
  "published": "2011-11-28T13:47:03.000Z",
  "updated": "2011-11-28T13:47:03.000Z",
  "title": "Tightness of Banach spaces and Baire category",
  "authors": [
    "Valentin Ferenczi",
    "Gilles Godefroy"
  ],
  "comment": "13 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove several dichotomies on linear embeddings between Banach spaces. Given an arbitrary Banach space X with a basis, we show that the relations of isomorphism and bi-embedding are meager or co-meager on the Polish set of block-subspaces of X. We relate this result with tightness and minimality of Banach spaces. Examples and open questions are provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-28T13:47:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "54E52"
    ],
    "keywords": [
      "baire category",
      "arbitrary banach space",
      "linear embeddings",
      "open questions",
      "isomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.6444F"
    }
  }
}