{
  "id": "1008.1151",
  "version": "v2",
  "published": "2010-08-06T09:42:28.000Z",
  "updated": "2012-10-09T12:57:06.000Z",
  "title": "On spectral approximation, Følner sequences and crossed products",
  "authors": [
    "Fernando Lledó"
  ],
  "comment": "15 pages; article partly rewritten, version to appear in J. Approx. Theory; changes w.r.t. v1: new introduction, results put in the context of spcetral approximation problems, only C*-crossed products are considered (instead of von Neumann crossed products; Eq.(3.6) of v1 deleted); more examples considered",
  "journal": "Journal of Approximation Theory 170 (2013) 155-171",
  "doi": "10.1016/j.jat.2012.10.003",
  "categories": [
    "math.OA",
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "In this article we study Foelner sequences for operators and mention their relation to spectral approximation problems. We construct a canonical Foelner sequence for the crossed product of a discrete amenable group $\\Gamma$ with a concrete C*-algebra A with a Foelner sequence. We also state a compatibility condition for the action of $\\Gamma$ on A. We illustrate our results with two examples: the rotation algebra (which contains interesting operators like almost Mathieu operators or periodic magnetic Schr\\\"odinger operators on graphs) and the C*-algebra generated by bounded Jacobi operators. These examples can be interpreted in the context of crossed products. The crossed products considered can be also seen as a more general frame that included the set of generalized band-dominated operators.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-09T12:57:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47L65",
      "46L60",
      "43A03"
    ],
    "keywords": [
      "crossed product",
      "følner sequences",
      "spectral approximation problems",
      "study foelner sequences",
      "compatibility condition"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.1151L"
    }
  }
}