{
  "id": "0904.0887",
  "version": "v1",
  "published": "2009-04-06T10:00:19.000Z",
  "updated": "2009-04-06T10:00:19.000Z",
  "title": "Extension of representations in quasi *-algebras",
  "authors": [
    "J. -P. Antoine",
    "F. Bagarello",
    "C. Trapani"
  ],
  "journal": "Ann. Inst. H. Poincar\\'e, {\\bf 69}, 241-264, (1998)",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let $(A, A_o)$ be a topological quasi *-algebra, which means in particular that $A_o$ is a topological *-algebra, dense in $A$. Let $\\pi^o$ be a *-representation of $A_o$ in some pre-Hilbert space ${\\cal D} \\subset {\\cal H}$. Then we present several ways of extending $\\pi^o$, by closure, to some larger quasi *-algebra contained in $A$, either by Hilbert space operators, or by sesquilinear forms on ${\\cal D}$. Explicit examples are discussed, both abelian and nonabelian, including the CCR algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-06T10:00:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "representations",
      "hilbert space operators",
      "pre-hilbert space",
      "larger quasi",
      "sesquilinear forms"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.0887A"
    }
  }
}