{
  "id": "1710.11265",
  "version": "v1",
  "published": "2017-10-30T22:49:33.000Z",
  "updated": "2017-10-30T22:49:33.000Z",
  "title": "Bounded Point Evaluations For Rationally Multicyclic Subnormal Operators",
  "authors": [
    "Liming Yang"
  ],
  "comment": "11 pages",
  "journal": "J. Math. Anal. Appl. (2018)",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $S$ be a pure bounded rationally multicyclic subnormal operator on a separable complex Hilbert space $\\mathcal H$ and let $M_z$ be the minimal normal extension on a separable complex Hilbert space $\\mathcal K$ containing $\\mathcal H.$ Let $bpe(S)$ be the set of bounded point evaluations and let $abpe(S)$ be the set of analytic bounded point evaluations. We show $abpe(S) = bpe(S) \\cap Int(\\sigma (S)).$ The result affirmatively answers a question asked by J. B. Conway concerning the equality of the interior of $bpe(S)$ and $abpe(S)$ for a rationally multicyclic subnormal operator $S.$ As a result, if $\\lambda_0\\in Int(\\sigma (S))$ and $dim(ker(S-\\lambda_0)^*) = N,$ where $N$ is the minimal number of cyclic vectors for $S,$ then the range of $S-\\lambda_0$ is closed, hence, $\\lambda_0 \\in \\sigma (S) \\setminus \\sigma_e (S).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-30T22:49:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded point evaluations",
      "separable complex hilbert space",
      "bounded rationally multicyclic subnormal operator",
      "pure bounded rationally multicyclic subnormal",
      "minimal normal extension"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}