{
  "id": "2207.02554",
  "version": "v1",
  "published": "2022-07-06T10:07:02.000Z",
  "updated": "2022-07-06T10:07:02.000Z",
  "title": "On Approximation Spaces and Greedy-type Bases",
  "authors": [
    "Pablo M. Berná",
    "Hung Viet Chu",
    "Eugenio Hernández"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The purpose of this paper is to introduce $\\omega$-Chebyshev-greedy and $\\omega$-partially greedy approximation classes and to study their relation with $\\omega$-approximation spaces, where the latter are a generalization of the classical approximation spaces. The relation gives us sufficient conditions of when certain continuous embeddings imply different greedy-type properties. Along the way, we generalize a result by P. Wojtaszczyk as well as characterize semi-greedy Schauder bases in quasi-Banach spaces, generalizing a previous result by the first author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-06T10:07:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "greedy-type bases",
      "partially greedy approximation classes",
      "characterize semi-greedy schauder bases",
      "first author",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}