{
  "id": "math/0502054",
  "version": "v3",
  "published": "2005-02-02T17:00:05.000Z",
  "updated": "2005-02-17T14:59:49.000Z",
  "title": "Minimality, homogeneity and topological 0-1 laws for subspaces of a Banach space",
  "authors": [
    "Valentin Ferenczi"
  ],
  "categories": [
    "math.FA",
    "math.CO"
  ],
  "abstract": "If a Banach space is saturated with basic sequences whose linear span embeds into the linear span of any subsequence, then it contains a minimal subspace. It follows that any Banach space is either ergodic or contains a minimal subspace. For a Banach space $X$ with an (unconditional) basis, topological 0-1 law type dichotomies are stated for block-subspaces of $X$ as well as for subspaces of $X$ with a successive FDD on its basis. A uniformity principle for properties of block-sequences, results about block-homogeneity, and a possible method to construct a Banach space with an unconditional basis, which has a complemented subspace without an unconditional basis, are deduced.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-02-17T14:59:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B03",
      "46B15"
    ],
    "keywords": [
      "banach space",
      "minimality",
      "homogeneity",
      "unconditional basis",
      "minimal subspace"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2054F"
    }
  }
}