{
  "id": "2403.16309",
  "version": "v1",
  "published": "2024-03-24T22:30:39.000Z",
  "updated": "2024-03-24T22:30:39.000Z",
  "title": "Multiplier algebras of $L^p$-operator algebras",
  "authors": [
    "Andrey Blinov",
    "Alonso Delfín",
    "Ellen Weld"
  ],
  "comment": "AMSLaTeX; 17 pages",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We show that the multiplier algebra of an approximately unital and nondegenerate $L^p$-operator algebra is again an $L^p$-operator algebra. We then investigate examples that drop both hypotheses. In particular, we show that the multiplier algebra of $T_2^p$, the algebra of strictly upper triangular $2\\times 2$ matrices acting on $\\ell_2^p$, is still an $L^p$-operator algebra for any $p$. To contrast this result, we provide a thorough study of the $L^1$-operator algebra $\\ell_0^1(G)$, the augmentation ideal of $\\ell^1(G)$ for a discrete group $G$, and then show that, at least when $G=\\mathbb{Z}/3\\mathbb{Z}$, its multiplier algebra is not an $L^p$-operator algebra for any $p \\in [1,\\infty)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-24T22:30:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46H15",
      "46H35",
      "47L10"
    ],
    "keywords": [
      "operator algebra",
      "multiplier algebra",
      "augmentation ideal",
      "thorough study",
      "discrete group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}