{
  "id": "1705.06062",
  "version": "v1",
  "published": "2017-05-17T09:22:56.000Z",
  "updated": "2017-05-17T09:22:56.000Z",
  "title": "Strict $K$-monotonicity and $K$-order continuity in symmetric spaces",
  "authors": [
    "Maciej Ciesielski"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper is devoted to strict $K$- monotonicity and $K$-order continuity in symmetric spaces. Using the local approach to the geometric structure in a symmetric space $E$ we investigate a connection between strict $K$-monotonicity and global convergence in measure of a sequence of the maximal functions. Next, we solve an essential problem whether an existence of a point of $K$-order continuity in a symmetric space $E$ on $[0,\\infty)$ implies that the embedding $E\\hookrightarrow{L^1}[0,\\infty)$ does not hold. We finish this article with a complete characterization of $K$-order continuity in a symmetric space $E$ that is written using a notion of order continuity under some assumptions on the fundamental function of $E$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-17T09:22:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "46B20",
      "46B42"
    ],
    "keywords": [
      "order continuity",
      "symmetric space",
      "monotonicity",
      "local approach",
      "essential problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}