{
  "id": "0712.3729",
  "version": "v1",
  "published": "2007-12-21T15:56:23.000Z",
  "updated": "2007-12-21T15:56:23.000Z",
  "title": "Passive systems with a normal main operator and quasi-selfadjoint systems",
  "authors": [
    "Yu. M. Arlinskiĭ",
    "S. Hassi",
    "H. S. V. de Snoo"
  ],
  "comment": "29 pages",
  "journal": "Complex Analysis and Operator Theory, 3 (2009), 19--56",
  "categories": [
    "math.FA",
    "math.SP"
  ],
  "abstract": "Passive systems $\\tau={T,M,N,H}$ with $M$ and $N$ as an input and output space and $H$ as a state space are considered in the case that the main operator on the state space is normal. Basic properties are given and a general unitary similarity result involving some spectral theoretic conditions on the main operator is established. A passive system $\\tau$ with $M=N$ is said to be quasi-selfadjoint if $ran(T-T^*)\\subset N$. The subclass $S^{qs}$ of the Schur class $S$ is the class formed by all transfer functions of quasi-selfadjoint passive systems. The subclass $S^{qs}$ is characterized and minimal passive quasi-selfadjoint realizations are studied. The connection between the transfer function belonging to the subclass $S^{qs}$ and the $Q$-function of $T$ is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-21T15:56:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A48",
      "47A56",
      "93B28",
      "93B15",
      "94C05"
    ],
    "keywords": [
      "passive system",
      "normal main operator",
      "quasi-selfadjoint systems",
      "state space",
      "transfer function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.3729A"
    }
  }
}