{
  "annotation_id": "1fdbf381-d731-490f-b72a-21ee6bf31e31",
  "date_created": "2026-02-17T05:53:23.070000Z",
  "date_modified": "2026-02-17T05:53:23.070000Z",
  "file_hash": "4ab8e103fa2075dde4f4765fd3a133c275b8bd7132c225bebb36f9e421cc288a",
  "private": false,
  "record": {
    "abstract": "The topology of the Moyal $*$-algebra may be defined in three ways: the algebra may be regarded as an operator algebra over the space of smooth declining functions either on the configuration space or on the phase space itself; or one may construct the $*$-algebra via a filtration of Hilbert spaces (or other Banach spaces) of distributions. We prove the equivalence of the three topologies thereby obtained. As a consequence, by filtrating the space of tempered distributions by Banach subspaces, we give new sufficient conditions for a phase-space function to correspond to a trace-class operator via the Weyl correspondence rule.",
    "arxiv_id": "2601.09934",
    "authors": [
      "Joseph C. V\u00e1rilly",
      "Jos\u00e9 M. Gracia-Bond\u00eda"
    ],
    "categories": [
      "math.OA",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1063/1.527984",
    "journal_ref": "J. Math. Phys. 29 (1988), 880-887",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra",
    "url": "https://arxiv.org/abs/2601.09934",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b6edb60f-fab7-40f3-9c93-939a0b53ba8b",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}