{
  "id": "math/0502239",
  "version": "v1",
  "published": "2005-02-11T14:18:07.000Z",
  "updated": "2005-02-11T14:18:07.000Z",
  "title": "Perturbation of Hausdorff moment sequences, and an application to the theory of C*-algebras of real rank zero",
  "authors": [
    "George A. Elliott",
    "Mikael Rordam"
  ],
  "comment": "23 pages",
  "journal": "Operator Algebras, The Abel Symposium 2004. Springer Verlag (2006), pp. 97-115",
  "categories": [
    "math.OA"
  ],
  "abstract": "We investigate the class of unital C*-algebras that admit a unital embedding into every unital C*-algebra of real rank zero, that has no finite-dimensional quotients. We refer to a C*-algebra in this class as an initial object. We show that there are many initial objects, including for example some unital, simple, infinite-dimensional AF-algebras, the Jiang-Su algebra, and the GICAR-algebra. That the GICAR-algebra is an initial object follows from an analysis of Hausdorff moment sequences. It is shown that a dense set of Hausdorff moment sequences belong to a given dense subgroup of the real numbers, and hence that the Hausdorff moment problem can be solved (in a non-trivial way) when the moments are required to belong to an arbitrary simple dimension group (i.e., unperforated simple ordered group with the Riesz decomposition property).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-02-11T14:18:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L35",
      "46L80",
      "44A60"
    ],
    "keywords": [
      "real rank zero",
      "initial object",
      "hausdorff moment sequences belong",
      "perturbation",
      "application"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2239E"
    }
  }
}