{
  "id": "2108.02168",
  "version": "v1",
  "published": "2021-08-04T16:51:12.000Z",
  "updated": "2021-08-04T16:51:12.000Z",
  "title": "On the commutant of $B(H)$ in its ultrapower",
  "authors": [
    "Emmanuel Chetcuti",
    "Beatriz Zamora-Aviles"
  ],
  "comment": "Comments are welcome!",
  "categories": [
    "math.FA",
    "math.LO"
  ],
  "abstract": "Let $B(H)$ be the algebra of bounded linear operators on a separable infinite-dimensional Hilbert space $H$. We study the commutant of $B(H)$ in its ultrapower. We characterize the class of non-principal ultrafilters for which this commutant is non-trivial. Additionally, we extend the class of ultrafilters for which the commutant is trivial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-04T16:51:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L05",
      "03E50"
    ],
    "keywords": [
      "ultrapower",
      "separable infinite-dimensional hilbert space",
      "bounded linear operators",
      "non-principal ultrafilters",
      "non-trivial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}