{
  "id": "0710.0038",
  "version": "v1",
  "published": "2007-09-29T03:13:46.000Z",
  "updated": "2007-09-29T03:13:46.000Z",
  "title": "Characterization of the matrix whose norm is determined by its action on decreasing sequences:The exceptional cases",
  "authors": [
    "Chang-Pao Chen",
    "Chun-Yen Shen",
    "Kuo-Zhong Wang"
  ],
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "Let $A=(a_{j,k})_{j,k \\ge 1}$ be a non-negative matrix. In this paper, we characterize those $A$ for which $\\|A\\|_{\\ell_p,\\ell_q}$ are determined by their actions on non-negative decreasing sequences, where one of $p$ and $q$ is 1 or $\\infty$. The conditions forcing on $A$ are sufficient and they are also necessary for non-negative finite matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-29T03:13:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A60",
      "47A30",
      "47B37"
    ],
    "keywords": [
      "exceptional cases",
      "characterization",
      "non-negative finite matrices",
      "non-negative decreasing sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.0038C"
    }
  }
}