{
  "id": "math/0101182",
  "version": "v2",
  "published": "2001-01-22T23:32:55.000Z",
  "updated": "2001-01-26T21:54:16.000Z",
  "title": "Invariance properties of thematic factorizations of matrix functions",
  "authors": [
    "R. B. Alexeev",
    "V. V. Peller"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA",
    "math.CA",
    "math.CV"
  ],
  "abstract": "We study the problem of invariance of indices of thematic factorizations. Such factorizations were introduced in [PY1] for studying superoptimal approximation by bounded analytic matrix functions. As shown in [PY1], the indices may depend on the choice of a thematic factorization. We introduce the notion of a monotone thematic factorization. The main result shows that under natural assumptions a matrix function that admits a thematic factorization also admits a monotone thematic factorization and the indices of a monotone thematic factorization are uniquely determined by the matrix function itself. We obtain similar results for so-called partial thematic factorizations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-01-26T21:54:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B35",
      "46E15",
      "30D55"
    ],
    "keywords": [
      "monotone thematic factorization",
      "invariance properties",
      "partial thematic factorizations",
      "bounded analytic matrix functions",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......1182A"
    }
  }
}