{
  "id": "1510.02723",
  "version": "v1",
  "published": "2015-10-09T16:09:26.000Z",
  "updated": "2015-10-09T16:09:26.000Z",
  "title": "Operator (quasi-)similarity, quasi-Hermitian operators and all that",
  "authors": [
    "Jean-Pierre Antoine",
    "Camillo Trapani"
  ],
  "comment": "16 pages. arXiv admin note: text overlap with arXiv:1409.3497, arXiv:1210.3163, arXiv:1307.5644",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity between operators and explore to what extent they preserve spectral properties. Then we study quasi-Hermitian operators, bounded or not, that is, operators that are quasi-similar to their adjoint and we discuss their application in pseudo-Hermitian quantum mechanics. Finally, we extend the analysis to operators in a partial inner product space (\\pip), in particular the scale of Hilbert spaces generated by a single unbounded metric operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-09T16:09:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.-w",
      "03.65.Ca",
      "02.30.Sa",
      "02.30.Tb"
    ],
    "keywords": [
      "pseudo-hermitian quantum mechanics",
      "similarity",
      "partial inner product space",
      "hilbert space",
      "single unbounded metric operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}