{
  "id": "0709.2946",
  "version": "v2",
  "published": "2007-09-19T02:43:58.000Z",
  "updated": "2009-09-12T04:05:38.000Z",
  "title": "The relationships between Invertible Module Maps X and X_z",
  "authors": [
    "Yun-Su Kim"
  ],
  "comment": "7 pages",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "If $R$ and $M$ are Hilbert modules (in the sense of R. G. Douglas and V. I. Paulsen), we study the relationship between invertible module maps $X:R\\to{M}$ and $X_{z}:R/R_{z}\\to{M/M_{z}}$. In particular, for quasi-free Hilbert modules $R$ and $M$, we provide a condition of a module map $X:R\\to{M}$, such that if $X_{z}:R/R_{z}\\to{M/M_{z}}$ is invertible for every $z$ in a domain $\\Omega$ in the complex plane, then $X$ is also invertible.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-12T04:05:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46C99",
      "46E20",
      "46B15"
    ],
    "keywords": [
      "invertible module maps",
      "relationship",
      "quasi-free hilbert modules",
      "complex plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.2946K"
    }
  }
}