{
  "id": "1509.08024",
  "version": "v1",
  "published": "2015-09-26T20:39:13.000Z",
  "updated": "2015-09-26T20:39:13.000Z",
  "title": "Duality for Unbounded Operators, and Applications",
  "authors": [
    "Palle Jorgensen",
    "Feng Tian"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise linking between such two Hilbert spaces when it is assumed that D is dense in one of the two; but generally not in the other. No relative boundedness is assumed. Nonetheless, under natural assumptions (motivated by potential theory), we prove a theorem where a comparison between the two Hilbert spaces is made via a specific selfadjoint semibounded operator. Applications include physical Hamiltonians, both continuous and discrete (infinite network models), and operator theory of reflection positivity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-26T20:39:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47L60",
      "46N30",
      "65R10",
      "58J65",
      "81S25"
    ],
    "keywords": [
      "unbounded operators",
      "hilbert space",
      "applications",
      "infinite network models",
      "specific selfadjoint semibounded operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150908024J"
    }
  }
}