{
  "id": "math/0603461",
  "version": "v2",
  "published": "2006-03-19T21:35:02.000Z",
  "updated": "2006-06-17T21:29:10.000Z",
  "title": "A remark on two duality relations",
  "authors": [
    "Emanuel Milman"
  ],
  "comment": "13 pages, typos corrected",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "We remark that an easy combination of two known results yields a positive answer, up to log(n) terms, to a duality conjecture that goes back to Pietsch. In particular, we show that for any two symmetric convex bodies K,T in R^n, denoting by N(K,T) the minimal number of translates of T needed to cover K, one has: N(K,T) <= N(T*,(C log(n))^{-1} K*)^{C log(n) loglog(n)}, where K*,T* are the polar bodies to K,T, respectively, and C > 1 is a universal constant. As a corollary, we observe a new duality result (up to log(n) terms) for Talagrand's \\gamma_p functionals.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-06-17T21:29:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "duality relations",
      "symmetric convex bodies",
      "results yields",
      "duality conjecture",
      "minimal number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3461M"
    }
  }
}