{
  "id": "1612.01145",
  "version": "v1",
  "published": "2016-12-04T17:16:13.000Z",
  "updated": "2016-12-04T17:16:13.000Z",
  "title": "Garling sequence spaces",
  "authors": [
    "Ben Wallis"
  ],
  "comment": "23 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "By generalizing a construction of Garling, for each $1\\leqslant p<\\infty$ and each normalized, nonincreasing sequence of positive numbers $w\\in c_0\\setminus\\ell_1$ we exhibit an $\\ell_p$-saturated, complementably homogeneous Banach space $g(w,p)$ related to the Lorentz sequence space $d(w,p)$. Using methods originally developed for studying $d(w,p)$, we show that $g(w,p)$ admits a unique (up to equivalence) subsymmetric basis, although when $w=(n^{-\\theta})_{n=1}^\\infty$ for some $0<\\theta<1$, it does not admit a symmetric basis. We then discuss some additional properties of $g(w,p)$ related to uniform convexity and superreflexivity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-04T17:16:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B25",
      "46B45",
      "46B04"
    ],
    "keywords": [
      "garling sequence spaces",
      "lorentz sequence space",
      "subsymmetric basis",
      "uniform convexity",
      "complementably homogeneous banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}