{
  "id": "1703.07772",
  "version": "v1",
  "published": "2017-03-22T17:58:00.000Z",
  "updated": "2017-03-22T17:58:00.000Z",
  "title": "On Garling sequence spaces",
  "authors": [
    "Fernando Albiac",
    "José L. Ansorena",
    "Ben Wallis"
  ],
  "comment": "25 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "The aim of this paper is to introduce and investigate a new class of separable Banach spaces modeled after an example of Garling from 1968. For each $1\\leqslant p<\\infty$ and each nonincreasing weight $\\textbf{w}\\in c_0\\setminus\\ell_1$ we exhibit an $\\ell_p$-saturated, complementably homogeneous, and uniformly subprojective Banach space $g(\\textbf{w},p)$. We also show that $g(\\textbf{w},p)$ admits a unique subsymmetric basis despite the fact that for a wide class of weights it does not admit a symmetric basis. This provides the first known examples of Banach spaces where those two properties coexist.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-22T17:58:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B25",
      "46B45",
      "46B03"
    ],
    "keywords": [
      "garling sequence spaces",
      "unique subsymmetric basis despite",
      "separable banach spaces",
      "uniformly subprojective banach space",
      "wide class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}