{
  "id": "1609.05301",
  "version": "v1",
  "published": "2016-09-17T08:53:18.000Z",
  "updated": "2016-09-17T08:53:18.000Z",
  "title": "Unbounded $p$-convergence in Lattice-Normed Vector Lattice",
  "authors": [
    "A. Aydın",
    "E. Yu. Emelyanov",
    "N. Erkurşun Özcan",
    "M. A. A. Marabeh"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "A net $x_\\alpha$ in a lattice-normed vector lattice $(X,p,E)$ is unbounded $p$-convergent to $x\\in X$, if $p(|x_\\alpha-x|\\wedge u)\\stackrel{{o}}\\to 0$ for every $u\\in X_+$. This convergence has been investigated recently for $(X,p,E)=(X,|\\cdot |,X)$ under the name of $uo$-convergence in \\cite{GTX}, for $(X,p,E)=(X,\\|\\cdot\\|,{\\mathbb R})$ under the name of $un$-convergence in \\cite{DOT,KMT}, and also for $(X,p,{\\mathbb R}^{X^*})$, where $p(x)[f]:=|f|(|x|)$ under the name $uaw$-convergence in \\cite{Z}. In this paper we study general properties of the unbounded $p$-convergence and of mixed-normed spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-17T08:53:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46A40",
      "46E30",
      "28A20"
    ],
    "keywords": [
      "lattice-normed vector lattice",
      "convergence",
      "study general properties",
      "convergent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}