{
  "id": "1202.3088",
  "version": "v3",
  "published": "2012-02-14T17:03:29.000Z",
  "updated": "2014-04-07T05:55:55.000Z",
  "title": "On the minimal space problem and a new result on existence of basic sequences in quasi-Banach spaces",
  "authors": [
    "Cleon S. Barroso"
  ],
  "comment": "A subtle mistake in the proof of main result makes obsolete the paper",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that if $X$ is a quasi-normed space which possesses an infinite countable dimensional subspace with a separating dual, then it admits a strictly weaker Hausdorff vector topology. Such a topology is constructed explicitly. As an immediate consequence, we obtain an improvement of a well-known result of Kalton-Shapiro and Drewnowski by showing that a quasi-Banach space contains a basic sequence if and only if it contains an infinite countable dimensional subspace whose dual is separating. We also use this result to highlight a new feature of the minimal quasi-Banach space constructed by Kalton. Namely, which all of its $\\aleph_0$-dimensional subspaces fail to have a separating family of continuous linear functionals.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-04-07T05:55:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasi-banach space",
      "minimal space problem",
      "basic sequence",
      "infinite countable dimensional subspace",
      "strictly weaker hausdorff vector topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.3088B"
    }
  }
}