{
  "id": "math/0601112",
  "version": "v3",
  "published": "2006-01-06T00:08:16.000Z",
  "updated": "2006-12-27T09:36:34.000Z",
  "title": "Random sets of isomorphism of linear operators on Hilbert space",
  "authors": [
    "Roman Vershynin"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/074921706000000815 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "IMS Lecture Notes Monograph Series 2006, Vol. 51, 148-154",
  "doi": "10.1214/074921706000000815",
  "categories": [
    "math.FA",
    "math.PR"
  ],
  "abstract": "This note deals with a problem of the probabilistic Ramsey theory in functional analysis. Given a linear operator $T$ on a Hilbert space with an orthogonal basis, we define the isomorphic structure $\\Sigma(T)$ as the family of all subsets of the basis so that $T$ restricted to their span is a nice isomorphism. Our main result is a dimension-free optimal estimate of the size of $\\Sigma(T)$. It improves and extends in several ways the principle of restricted invertibility due to Bourgain and Tzafriri. With an appropriate notion of randomness, we obtain a randomized principle of restricted invertibility.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-12-27T09:36:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B09",
      "47D25"
    ],
    "keywords": [
      "hilbert space",
      "linear operator",
      "random sets",
      "probabilistic ramsey theory",
      "dimension-free optimal estimate"
    ],
    "tags": [
      "monograph",
      "journal article",
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1112V"
    }
  }
}