{
  "id": "2211.03441",
  "version": "v1",
  "published": "2022-11-07T10:43:40.000Z",
  "updated": "2022-11-07T10:43:40.000Z",
  "title": "Convexity in the interpolation spaces",
  "authors": [
    "Daher Mohammad"
  ],
  "comment": "15 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this work we study if the norms rotund, uniformly rotund, weakly uniformly rotund, locally uniformly rotund or weakly locally uniformly rotund interpolate in the complex or the real interpolation spaces. We will see that the properties uniformly rotund and weakly uniformly rotund interpolate, but the properties locally uniformly rotund or weakly locally uniformly rotund do not interpolate in general except for the dual interpolation couple.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-07T10:43:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B70"
    ],
    "keywords": [
      "dual interpolation couple",
      "real interpolation spaces",
      "weakly locally uniformly rotund interpolate",
      "properties locally uniformly rotund",
      "weakly uniformly rotund interpolate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}