{
  "id": "math/0611045",
  "version": "v1",
  "published": "2006-11-02T10:05:51.000Z",
  "updated": "2006-11-02T10:05:51.000Z",
  "title": "A canonical decomposition for linear operators and linear relations",
  "authors": [
    "S. Hassi",
    "Z. Sebestyén",
    "H. S. V. de Snoo",
    "F. H. Szafraniec"
  ],
  "comment": "to appear in Acta Math. Hungarica, volume 116(1-2)",
  "categories": [
    "math.FA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "An arbitrary linear relation (multivalued operator) acting from one Hilbert space to another Hilbert space is shown to be the sum of a closable operator and a singular relation whose closure is the Cartesian product of closed subspaces. This decomposition can be seen as an analog of the Lebesgue decomposition of a measure into a regular part and a singular part. The two parts of a relation are characterized metrically and in terms of Stone's characteristic projection onto the closure of the linear relation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-02T10:05:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A05",
      "47A06"
    ],
    "keywords": [
      "linear operators",
      "canonical decomposition",
      "hilbert space",
      "stones characteristic projection",
      "arbitrary linear relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11045H"
    }
  }
}