{
  "id": "1410.8786",
  "version": "v1",
  "published": "2014-10-31T16:02:25.000Z",
  "updated": "2014-10-31T16:02:25.000Z",
  "title": "Localization and Projections on Bi--Parameter BMO",
  "authors": [
    "Richard Lechner",
    "Paul F. X. Müller"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that for any operator T on bi--parameter BMO the identity factors through T or Id - T. As a consequence, bi--parameter BMO is a primary Banach space. Bourgain's localization method provides the conceptual framework of our proof. It consists in replacing the factorization problem on the non--separable Banach space bi--parameter BMO by its localized, finite dimensional counterpart. We solve the resulting finite dimensional factorization problems by combinatorics of colored dyadic rectangles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-31T16:02:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B25",
      "60G46",
      "46B07",
      "46B26",
      "30H35"
    ],
    "keywords": [
      "resulting finite dimensional factorization problems",
      "non-separable banach space bi-parameter bmo",
      "projections",
      "bourgains localization method",
      "finite dimensional counterpart"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.8786L"
    }
  }
}