{
  "id": "1308.2510",
  "version": "v1",
  "published": "2013-08-12T10:05:14.000Z",
  "updated": "2013-08-12T10:05:14.000Z",
  "title": "Direct integrals of matrices",
  "authors": [
    "Piotr Niemiec"
  ],
  "comment": "15 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "It is shown that each linear operator on a separable Hilbert space which generates a finite type I von Neumann algebra has, up to unitary equivalence, a unique representation as a direct integral of inflations of mutually unitary inequivalent irreducible matrices. This leads to a simplification of the so-called prime (or central) decomposition and the multiplicity theory for such operators. The concept of so-called p-isomorphisms between special classes of such operators is discussed. All results are formulated in more general settings; that is, for tuples of closed densely defined operators affiliated with finite type I von Neumann algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-12T10:05:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B40",
      "47C15"
    ],
    "keywords": [
      "direct integral",
      "von neumann algebra",
      "finite type",
      "densely defined operators",
      "mutually unitary inequivalent irreducible matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.2510N"
    }
  }
}