{
  "id": "2004.12751",
  "version": "v1",
  "published": "2020-04-27T12:51:17.000Z",
  "updated": "2020-04-27T12:51:17.000Z",
  "title": "The complement of M(a) in H(b)",
  "authors": [
    "Maria Teresa Nowak Paweł Sobolewski Andrzej Sołtysiak"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $b$ be a nonextreme function in the unit ball of $H^{\\infty}$ on the unit disk $\\mathbb{D} $ and let $a$ be an outer $H^{\\infty}$ function such that $|a|^2+|b|^2=1$ almost everywhere on $\\partial \\mathbb{D}$. The sufficient and necessary conditions for the orthogonal complement of $\\mathcal{M}(a)$ in $\\mathcal{H}(b)$ be finite dimensional has been given by D. Sarason . Here we describe this space explicitly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-27T12:51:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E22",
      "47B32",
      "30H05"
    ],
    "keywords": [
      "nonextreme function",
      "unit ball",
      "unit disk",
      "necessary conditions",
      "orthogonal complement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}