{
  "id": "math/9312208",
  "version": "v1",
  "published": "1993-12-29T17:04:17.000Z",
  "updated": "1993-12-29T17:04:17.000Z",
  "title": "Proportional subspaces of spaces with unconditional basis have good volume properties",
  "authors": [
    "Marius Junge"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "A generalization of Lozanovskii's result is proved. Let E be $k$-dimensional subspace of an $n$-dimensional Banach space with unconditional basis. Then there exist $x_1,..,x_k \\subset E$ such that $B_E \\p \\subset \\p absconv\\{x_1,..,x_k\\}$ and \\[ \\kla \\frac{{\\rm vol}(absconv\\{x_1,..,x_k\\})}{{\\rm vol}(B_E)} \\mer^{\\frac{1}{k}} \\kl \\kla e\\p \\frac{n}{k} \\mer^2 \\pl .\\] This answers a question of V. Milman which appeared during a GAFA seminar talk about the hyperplane problem. We add logarithmical estimates concerning the hyperplane conjecture for proportional subspaces and quotients of Banach spaces with unconditional basis. File Length:27K",
  "revisions": [
    {
      "version": "v1",
      "updated": "1993-12-29T17:04:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unconditional basis",
      "proportional subspaces",
      "volume properties",
      "gafa seminar talk",
      "dimensional banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1993math.....12208J"
    }
  }
}