{
  "id": "2012.13437",
  "version": "v1",
  "published": "2020-12-24T20:21:54.000Z",
  "updated": "2020-12-24T20:21:54.000Z",
  "title": "Higher projective tensor products of $c_0$",
  "authors": [
    "R. M. Causey",
    "Stephen J. Dilworth"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $m,n$ be positive integers with $m<n$. Under certain assumptions on the Banach space $X$, we prove that the $n$-fold projective tensor product of $X$, $\\widehat{\\otimes}^n_\\pi X$, is not isomorphic to any subspace of any quotient of the $m$-fold projective tensor product, $\\widehat{\\otimes}_\\pi^m X$. In particular, we prove that $\\widehat{\\otimes}^n_\\pi c_0$ is not isomorphic to any subspace of any quotient of $\\widehat{\\otimes}_\\pi^m c_0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-24T20:21:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higher projective tensor products",
      "fold projective tensor product",
      "isomorphic",
      "banach space",
      "assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}