{
  "id": "0906.3253",
  "version": "v2",
  "published": "2009-06-17T17:33:30.000Z",
  "updated": "2010-02-08T21:47:39.000Z",
  "title": "Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators",
  "authors": [
    "Daniel Carando",
    "Daniel Galicer"
  ],
  "comment": "23 pages",
  "journal": "Quart. J. Math. 62 (2011), 845--869",
  "doi": "10.1093/qmath/haq024",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study tensor norms that destroy unconditionality in the following sense: for every Banach space $E$ with unconditional basis, the $n$-fold tensor product of $E$ (with the corresponding tensor norm) does not have unconditional basis. We establish an easy criterion to check weather a tensor norm destroys unconditionality or not. Using this test we get that all injective and projective tensor norms different from $\\varepsilon$ and $\\pi$ destroy unconditionality, both in full and symmetric tensor products. We present applications to polynomial ideals: we show that many usual polynomial ideals never enjoy the Gordon-Lewis property. We also consider the unconditionality of the monomial basic sequence. Analogous problems for multilinear and operator ideals are addressed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-02-08T21:47:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46M05",
      "46G25",
      "47L20"
    ],
    "keywords": [
      "multilinear forms",
      "destroy unconditionality",
      "unconditional basis",
      "tensor norm destroys unconditionality",
      "usual polynomial ideals"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.3253C"
    }
  }
}