{
  "id": "2405.19579",
  "version": "v1",
  "published": "2024-05-30T00:07:22.000Z",
  "updated": "2024-05-30T00:07:22.000Z",
  "title": "Duality between Y-convexity and $Y^{\\times}$-concavity of linear operators between Banach lattices",
  "authors": [
    "José Luis Hernández-Barradas",
    "Fernando Galaz-Fontes"
  ],
  "comment": "31 pages. arXiv admin note: text overlap with arXiv:2311.01124",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we study the Y-convexity, a property which is obtained by considering a real Banach sequence lattice Y instead of $\\ell^p$ for a linear operator $T : E \\rightarrow X$, where E is a Banach space and X is a Banach lattice. We introduce some vector sequence spaces in order to characterize the Y-convexity of T by means of the continuity of an associated operator $\\overline{T}$. Analogous results for Y-concavity are also obtained. Finally, the duality between Y-convexity and $Y^{\\times}$-concavity is proven.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-30T00:07:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B42",
      "47A30",
      "47B10"
    ],
    "keywords": [
      "linear operator",
      "banach lattice",
      "y-convexity",
      "real banach sequence lattice",
      "vector sequence spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}