{
  "id": "math/9906106",
  "version": "v2",
  "published": "1999-06-15T16:23:54.000Z",
  "updated": "2002-03-28T19:53:03.000Z",
  "title": "On Graded K-theory, Elliptic Operators and the Functional Calculus",
  "authors": [
    "Jody Trout"
  ],
  "comment": "14 pages texed",
  "journal": "Illinois Journal of Mathematics, 44 No. 2 (Summer 2000) 294-309",
  "categories": [
    "math.OA",
    "math.KT"
  ],
  "abstract": "Let $A$ be a graded C*-algebra. We characterize Kasparov's K-theory group $\\hat{K}_0(A)$ in terms of graded *-homomorphisms by proving a general converse to the functional calculus theorem for self-adjoint regular operators on graded Hilbert modules. An application to the index theory of elliptic differential operators on smooth closed manifolds and asymptotic morphisms is discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-03-28T19:53:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic operators",
      "graded k-theory",
      "characterize kasparovs k-theory group",
      "self-adjoint regular operators",
      "functional calculus theorem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......6106T"
    }
  }
}