{
  "id": "math/0611349",
  "version": "v2",
  "published": "2006-11-12T12:45:05.000Z",
  "updated": "2008-02-18T14:04:59.000Z",
  "title": "Injective and projective Hilbert C*-modules, and C*-algebras of compact operators",
  "authors": [
    "Michael Frank",
    "Vern I. Paulsen"
  ],
  "comment": "28 pages, Proposition 3.4 corrected after receiving remarks from Hanfeng Li, thanks for pointing out the errors. Some minor corrections in formulations. 15 references added",
  "categories": [
    "math.OA",
    "math.KT"
  ],
  "abstract": "We consider projectivity and injectivity of Hilbert C*-modules in the categories of Hilbert C*-(bi-)modules over a fixed C*-algebra of coefficients (and another fixed C*-algebra represented as bounded module operators) and bounded (bi-)module morphisms, either necessarily adjointable or arbitrary ones. As a consequence of these investigations, we obtain a set of equivalent conditions characterizing C*-subalgebras of C*-algebras of compact operators on Hilbert spaces in terms of general properties of Hilbert C*-modules over them. Our results complement results recently obtained by B. Magajna, J. Schweizer and M. Kusuda. In particular, all Hilbert C*-(bi-)modules over C*-algebras of compact operators on Hilbert spaces are both injective and projective in the categories we consider. For more general C*-algebras we obtain classes of injective and projective Hilbert C*-(bi-)modules.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-02-18T14:04:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L08",
      "46H25"
    ],
    "keywords": [
      "compact operators",
      "projective hilbert",
      "hilbert spaces",
      "results complement results",
      "categories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11349F"
    }
  }
}