{
  "id": "1903.01763",
  "version": "v1",
  "published": "2019-03-05T10:42:15.000Z",
  "updated": "2019-03-05T10:42:15.000Z",
  "title": "A remark on approximation with polynomials and greedy bases",
  "authors": [
    "Pablo M. Berná",
    "Antonio Pérez"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We investigate properties of the $m$-th error of approximation by polynomials with constant coefficients $\\mathcal{D}_{m}(x)$ and with modulus-constant coefficients $\\mathcal{D}_{m}^{\\ast}(x)$ introduced by Bern\\'a and Blasco (2016) to study greedy bases in Banach spaces. We characterize when $\\liminf_{m}{\\mathcal{D}_{m}(x)}$ and $\\liminf_{m}{\\mathcal{D}_{m}^*(x)}$ are equivalent to $\\| x\\|$ in terms of the democracy and superdemocracy functions, and provide sufficient conditions ensuring that $\\lim_{m}{\\mathcal{D}_{m}^*(x)} = \\lim_{m}{\\mathcal{D}_{m}(x)} = \\| x\\|$, extending previous very particular results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-05T10:42:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomials",
      "approximation",
      "study greedy bases",
      "sufficient conditions",
      "modulus-constant coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}