{
  "id": "math/0504304",
  "version": "v1",
  "published": "2005-04-14T18:48:27.000Z",
  "updated": "2005-04-14T18:48:27.000Z",
  "title": "Operator Holes and extensions of sectorial operators and dual pairs of contractions",
  "authors": [
    "Mark Malamud"
  ],
  "categories": [
    "math.FA",
    "math.SP"
  ],
  "abstract": "A description of the set of $m$-sectorial extensions of a dual pair $\\{A_1,A_2\\}$ of nonnegative operators is obtained. Some classes of nonaccretive extensions of the dual pair $\\{A_1,A_2\\}$ are described too. Both problems are reduced to similar problems for a dual pair $\\{T_1,T_2\\}$ of nondensely defined symmetric contractions $T_j=(I-A_j)(I+A_j)^{-1},\\ j\\in\\{1,2\\}$. In turn these problems are reduced to the investigation of the corresponding operator \"holes\". A complete description of the set of all proper and improper extensions of a nonnegative operator is obtained too.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-04-14T18:48:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A57",
      "47B25"
    ],
    "keywords": [
      "dual pair",
      "sectorial operators",
      "operator holes",
      "nonnegative operator",
      "sectorial extensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4304M"
    }
  }
}