{
  "id": "1110.4253",
  "version": "v2",
  "published": "2011-10-19T12:10:33.000Z",
  "updated": "2011-10-27T14:24:31.000Z",
  "title": "General forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series",
  "authors": [
    "Vladimir A. Mikhailets",
    "Aleksandr A. Murach"
  ],
  "comment": "in English, translation of the 1-st (Russian) version, 12 pages",
  "journal": "Methods Funct. Anal. Topology 17 (2011), no. 4, 330-340",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that the classical Menshov-Rademacher, Orlicz, and Tandori theorems remain true for orthogonal series given in the direct integrals of measurable collections of Hilbert spaces. In particular, these theorems are true for the spaces L_{2}(X,d\\mu;H) of vector-valued functions, where (X,\\mu) is an arbitrary measure space, and H is a real or complex Hilbert space of an arbitrary dimension.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-27T14:24:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "40A30",
      "46E40"
    ],
    "keywords": [
      "orthogonal series",
      "general forms",
      "menshov-rademacher",
      "tandori theorems remain true",
      "complex hilbert space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.4253M"
    }
  }
}