{
  "id": "1506.03397",
  "version": "v1",
  "published": "2015-06-10T17:09:32.000Z",
  "updated": "2015-06-10T17:09:32.000Z",
  "title": "Characterization of $1$-almost greedy bases",
  "authors": [
    "F. Albiac",
    "J. L. Ansorena"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "This article closes the cycle of characterizations of greedy-like bases in the isometric case initiated in [F. Albiac and P. Wojtaszczyk, Characterization of $1$-greedy bases, J. Approx. Theory 138 (2006)] with the characterization of $1$-greedy bases and continued in [F. Albiac and J. L. Ansorena, Characterization of $1$-quasi-greedy bases, arXiv:1504.04368v1 [math.FA] (2015)] with the characterization of $1$-quasi-greedy bases. Here we settle the problem of providing a characterization of $1$-almost greedy bases in (real or complex) Banach spaces. We show that a (semi-normalized) basis in a Banach space is almost-greedy with almost greedy constant equal to $1$ if and only if it is quasi-greedy with suppression quasi-greedy constant equal to $1$ and has Property (A).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-10T17:09:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B15",
      "41A65",
      "46B15"
    ],
    "keywords": [
      "characterization",
      "suppression quasi-greedy constant equal",
      "quasi-greedy bases",
      "banach space",
      "isometric case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150603397A"
    }
  }
}