{
  "id": "2501.10545",
  "version": "v1",
  "published": "2025-01-17T20:38:55.000Z",
  "updated": "2025-01-17T20:38:55.000Z",
  "title": "Sesquilinear forms as eigenvectors in quasi *-algebras, with an application to ladder elements",
  "authors": [
    "Fabio Bagarello",
    "Hiroshi Inoue",
    "Salvatore Triolo"
  ],
  "comment": "In press in Mathematische Nachrichten",
  "categories": [
    "math-ph",
    "math.MP",
    "math.OA"
  ],
  "abstract": "We consider a particular class of sesquilinear forms on a {Banach quasi *-algebra} $(\\A[\\|.\\|],\\Ao[\\|.\\|_0])$ which we call {\\em eigenstates of an element} $a\\in\\A$, and we deduce some of their properties. We further apply our definition to a family of ladder elements, i.e. elements of $\\A$ obeying certain commutation relations physically motivated, and we discuss several results, including orthogonality and biorthogonality of the forms, via GNS-representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-17T20:38:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sesquilinear forms",
      "ladder elements",
      "application",
      "eigenvectors",
      "banach quasi"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}