{
  "id": "2011.05835",
  "version": "v1",
  "published": "2020-11-11T14:59:27.000Z",
  "updated": "2020-11-11T14:59:27.000Z",
  "title": "$k-$smoothness on polyhedral Banach spaces",
  "authors": [
    "Subhrajit Dey",
    "Arpita Mal",
    "Kallol Paul"
  ],
  "comment": "11 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We characterize $k-$smoothness of an element on the unit sphere of a finite-dimensional polyhedral Banach space. Then we study $k-$smoothness of an operator $T \\in \\mathbb{L}(\\ell_{\\infty}^n,\\mathbb{Y}),$ where $\\mathbb{Y}$ is a two-dimensional Banach space with the additional condition that $T$ attains norm at each extreme point of $B_{\\ell_{\\infty}^{n}}.$ We also characterize $k-$smoothness of an operator defined between $\\ell_{\\infty}^3$ and $\\ell_{1}^3.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-11T14:59:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "47L05"
    ],
    "keywords": [
      "smoothness",
      "finite-dimensional polyhedral banach space",
      "two-dimensional banach space",
      "unit sphere",
      "additional condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}