{
  "id": "2003.09878",
  "version": "v1",
  "published": "2020-03-22T12:41:08.000Z",
  "updated": "2020-03-22T12:41:08.000Z",
  "title": "$c_{0} \\widehat{\\otimes}_πc_{0}\\widehat{\\otimes}_πc_{0}$ is not isomorphic to a subspace of $c_{0} \\widehat{\\otimes}_πc_{0}$",
  "authors": [
    "R. M. Causey",
    "E. Galego",
    "C. Samuel"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In the present paper we prove that the $3$-fold projective tensor product of $c_0$, $c_{0} \\widehat{\\otimes}_\\pi c_{0}\\widehat{\\otimes}_\\pi c_{0}$, is not isomorphic to a subspace of $c_{0} \\widehat{\\otimes}_\\pi c_{0}$. In particular, this settles the long-standing open problem of whether $c_{0} \\widehat{\\otimes}_\\pi c_{0}$ is isomorphic to $c_{0} \\widehat{\\otimes}_\\pi c_{0}\\widehat{\\otimes}_\\pi c_{0}$. The origin of this problem goes back to Joe Diestel who mentioned it in a private communication to the authors of paper \"Unexpected subspaces of tensor products\" published in 2006.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-22T12:41:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "isomorphic",
      "fold projective tensor product",
      "long-standing open problem",
      "joe diestel",
      "private communication"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}