{
  "id": "2307.15632",
  "version": "v1",
  "published": "2023-07-28T15:44:18.000Z",
  "updated": "2023-07-28T15:44:18.000Z",
  "title": "Commutative $G$-invariant Toeplitz C$^\\ast$ algebras on the Fock space and their Gelfand theory through Quantum Harmonic Analysis",
  "authors": [
    "Robert Fulsche",
    "Miguel Angel Rodriguez Rodriguez"
  ],
  "comment": "26 pages; Comments are welcome",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We discuss the notion of spectral synthesis for the setting of Quantum Harmonic Analysis. Using these concepts, we study subalgebras of the full Toeplitz algebra with certain invariant symbols and their commutators. In particular, we find a new class of commutative Toeplitz C$^\\ast$ algebras on the Fock space. In the end, we investigate the Gelfand theory of those commutative C$^\\ast$ algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-28T15:44:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47L80",
      "47B35",
      "30H20"
    ],
    "keywords": [
      "quantum harmonic analysis",
      "fock space",
      "gelfand theory",
      "invariant toeplitz",
      "commutative"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}