{
  "id": "math/9812160",
  "version": "v1",
  "published": "1998-12-30T16:25:57.000Z",
  "updated": "1998-12-30T16:25:57.000Z",
  "title": "Embeddings of Banach Spaces into Banach Lattices and the Gordon-Lewis Property",
  "authors": [
    "Peter G. Casazza",
    "N. J. Nielsen"
  ],
  "comment": "32 pages, latex2e",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we first show that if $X$ is a Banach space and $\\alpha$ is a left invariant crossnorm on $\\ell_\\infty\\otimes X$, then there is a Banach lattice $L$ and an isometric embedding $J$ of $X$ into $L$, so that $I\\otimes J$ becomes an isometry of $\\ell_\\infty\\otimes_\\alpha X$ onto $\\ell_\\infty\\otimes_m J(X)$. Here $I$ denotes the identity operator on $\\ell_\\infty$ and $\\ell_\\infty\\otimes_m J(X)$ the canonical lattice tensor product. This result is originally due to G. Pisier (unpublished), but our proof is different. We then use this to characterize the Gordon-Lewis property $\\GL$ in terms of embeddings into Banach lattices. Also other structures related to the $\\GL$ are investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-12-30T16:25:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B40",
      "46B42"
    ],
    "keywords": [
      "banach lattice",
      "banach space",
      "gordon-lewis property",
      "left invariant crossnorm",
      "canonical lattice tensor product"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....12160C"
    }
  }
}