{
  "id": "1403.3777",
  "version": "v1",
  "published": "2014-03-15T09:45:09.000Z",
  "updated": "2014-03-15T09:45:09.000Z",
  "title": "Renorming spaces with greedy bases",
  "authors": [
    "S. J. Dilworth",
    "D. Kutzarova",
    "E. Odell",
    "Th. Schlumprecht",
    "A. Zsák"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the problem of improving the greedy constant or the democracy constant of a basis of a Banach space by renorming. We prove that every Banach space with a greedy basis can be renormed, for a given $\\vare>0$, so that the basis becomes $(1+\\vare)$-democratic, and hence $(2+\\vare)$-greedy, with respect to the new norm. If in addition the basis is bidemocratic, then there is a renorming so that in the new norm the basis is $(1+\\vare)$-greedy. We also prove that in the latter result the additional assumption of the basis being bidemocratic can be removed for a large class of bases. Applications include the Haar systems in $L_p[0,1]$, $1<p<\\infty$, and in dyadic Hardy space $H_1$, as well as the unit vector basis of Tsirelson space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-15T09:45:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A65",
      "41A44",
      "41A50",
      "46B03"
    ],
    "keywords": [
      "greedy bases",
      "renorming spaces",
      "banach space",
      "unit vector basis",
      "dyadic hardy space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.3777D"
    }
  }
}