{
  "id": "0902.3483",
  "version": "v1",
  "published": "2009-02-19T23:12:54.000Z",
  "updated": "2009-02-19T23:12:54.000Z",
  "title": "Weak operator topology, operator ranges and operator equations via Kolmogorov widths",
  "authors": [
    "M. I. Ostrovskii",
    "V. S. Shulman"
  ],
  "journal": "Integral Equations and Operator Theory 65 (2009), 551-572",
  "doi": "10.1007/s00020-009-1691-0",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Let $K$ be an absolutely convex infinite-dimensional compact in a Banach space $\\mathcal{X}$. The set of all bounded linear operators $T$ on $\\mathcal{X}$ satisfying $TK\\supset K$ is denoted by $G(K)$. Our starting point is the study of the closure $WG(K)$ of $G(K)$ in the weak operator topology. We prove that $WG(K)$ contains the algebra of all operators leaving $\\overline{\\lin(K)}$ invariant. More precise results are obtained in terms of the Kolmogorov $n$-widths of the compact $K$. The obtained results are used in the study of operator ranges and operator equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-19T23:12:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A05",
      "41A46",
      "47A30",
      "47A62"
    ],
    "keywords": [
      "weak operator topology",
      "operator equations",
      "operator ranges",
      "kolmogorov widths",
      "absolutely convex infinite-dimensional compact"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.3483O"
    }
  }
}