{
  "id": "2103.05352",
  "version": "v1",
  "published": "2021-03-09T11:01:19.000Z",
  "updated": "2021-03-09T11:01:19.000Z",
  "title": "The multiplier algebra of the noncommutative Schwartz space",
  "authors": [
    "Tomasz Ciaś",
    "Krzysztof Piszczek"
  ],
  "journal": "Banach J. Math. Anal. 11 (2017), no. 3, 615-635",
  "doi": "10.1215/17358787-2017-0007",
  "categories": [
    "math.FA"
  ],
  "abstract": "We describe the multiplier algebra of the noncommutative Schwartz space. This multiplier algebra can be seen as the largest ${}^*$-algebra of unbounded operators on a separable Hilbert space with the classical Schwartz space of rapidly decreasing functions as the domain. We show in particular that it is neither a $\\mathcal{Q}$-algebra nor $m$-convex. On the other hand, we prove that classical tools of functional analysis, for example, the closed graph theorem, the open mapping theorem or the uniform boundedness principle, are still available.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-09T11:01:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47L10",
      "46K10",
      "46H15",
      "46A13",
      "46A11"
    ],
    "keywords": [
      "noncommutative schwartz space",
      "multiplier algebra",
      "uniform boundedness principle",
      "separable hilbert space",
      "functional analysis"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}