{
  "id": "2004.09435",
  "version": "v1",
  "published": "2020-04-20T16:43:25.000Z",
  "updated": "2020-04-20T16:43:25.000Z",
  "title": "On the properties of quasi-Banach function spaces",
  "authors": [
    "Aleš Nekvinda",
    "Dalimil Peša"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we explore some basic properties of quasi-Banach function spaces which are important in applications. Namely, we show that they posses a generalised version of Riesz--Fischer property, that embeddings between them are always continuous and that the dilation operator is bounded on them. We also provide a characterisation of separability for quasi-Banach function spaces over the Euclidean space. Furthermore, we extend the classical Riesz--Fischer theorem to the context of quasinormed spaces and, as a consequence, obtain an alternative proof of completeness of quasi-Banach function spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-20T16:43:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46A16",
      "46E30"
    ],
    "keywords": [
      "quasi-banach function spaces",
      "basic properties",
      "dilation operator",
      "euclidean space",
      "classical riesz-fischer theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}