{
  "id": "math/0407238",
  "version": "v1",
  "published": "2004-07-14T19:37:33.000Z",
  "updated": "2004-07-14T19:37:33.000Z",
  "title": "On convexified packing and entropy duality",
  "authors": [
    "S. Artstein",
    "V. Milman",
    "S. J. Szarek",
    "N. Tomczak-Jaegermann"
  ],
  "comment": "6 p., LATEX",
  "journal": "Geom. Funct. Anal. 14 (2004), no. 5, 1134-1141.",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "A 1972 duality conjecture due to Pietsch asserts that the entropy numbers of a compact operator acting between two Banach spaces and those of its adjoint are (in an appropriate sense) equivalent. This is equivalent to a dimension free inequality relating covering (or packing) numbers for convex bodies to those of their polars. The duality conjecture has been recently proved (see math.FA/0407236) in the central case when one of the Banach spaces is Hilbertian, which - in the geometric setting - corresponds to a duality result for symmetric convex bodies in Euclidean spaces. In the present paper we define a new notion of \"convexified packing,\" show a duality theorem for that notion, and use it to prove the duality conjecture under much milder conditions on the spaces involved (namely, that one of them is K-convex).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-07-14T19:37:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B10",
      "46B07",
      "46B50",
      "47A05",
      "52C17",
      "51F99"
    ],
    "keywords": [
      "entropy duality",
      "convexified packing",
      "duality conjecture",
      "banach spaces",
      "symmetric convex bodies"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7238A"
    }
  }
}