{
  "id": "2208.10203",
  "version": "v1",
  "published": "2022-08-22T11:01:29.000Z",
  "updated": "2022-08-22T11:01:29.000Z",
  "title": "Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including Besov spaces",
  "authors": [
    "Fernando Albiac",
    "José L. Ansorena",
    "Glenier Bello",
    "Przemysław Wojtaszczyk"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that the sequence spaces $\\ell_p\\oplus\\ell_q$ and the spaces of infinite matrices $\\ell_p(\\ell_q)$, $\\ell_q(\\ell_p)$ and $(\\bigoplus_{n=1}^\\infty \\ell_p^n)_{\\ell_q}$, which are isomorphic to certain Besov spaces, have an almost greedy basis whenever $0<p<1<q<\\infty$. More precisely, we custom-build almost greedy bases in such a way that the Lebesgue parameters grow in a prescribed manner. Our arguments critically depend on the extension of the Dilworth-Kalton-Kutzarova method from [S. J. Dilworth, N. J. Kalton, and D. Kutzarova, On the existence of almost greedy bases in Banach spaces, Studia Math. 159 (2003), no. 1, 67-101], which was originally designed for constructing almost greedy bases in Banach spaces, to make it valid for direct sums of mixed-normed spaces with nonlocally convex components. Additionally, we prove that the fundamental functions of all almost greedy bases of these spaces grow as $(m^{1/q})_{m=1}^\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-22T11:01:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B15",
      "41A65"
    ],
    "keywords": [
      "greedy basis",
      "besov spaces",
      "mixed-norm sequence",
      "matrix spaces",
      "banach spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}