{
  "id": "1602.02546",
  "version": "v1",
  "published": "2016-02-08T12:40:14.000Z",
  "updated": "2016-02-08T12:40:14.000Z",
  "title": "Completion and extension of operators in Kreĭn spaces",
  "authors": [
    "D. Baidiuk"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1403.5133",
  "categories": [
    "math.FA"
  ],
  "abstract": "A generalization of the well-known results of M.G. Kre\\u{\\i}n about the description of selfadjoint contractive extension of a hermitian contraction is obtained. This generalization concerns the situation, where the selfadjoint operator $A$ and extensions $\\widetilde A$ belong to a Kre\\u{\\i}n space or a Pontryagin space and their defect operators are allowed to have a fixed number of negative eigenvalues. Also a result of Yu.L. Shmul'yan on completions of nonnegative block operators is generalized for block operators with a fixed number of negative eigenvalues in a Kre\\u{\\i}n space. This paper is a natural continuation of S. Hassi's and author's paper [5].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-08T12:40:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46C20",
      "47A20",
      "47A63",
      "47B25"
    ],
    "keywords": [
      "kreĭn spaces",
      "completion",
      "negative eigenvalues",
      "fixed number",
      "selfadjoint contractive extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160202546B"
    }
  }
}