{
  "id": "1609.05326",
  "version": "v1",
  "published": "2016-09-17T12:40:24.000Z",
  "updated": "2016-09-17T12:40:24.000Z",
  "title": "Preduals and complementation of spaces of bounded linear operators",
  "authors": [
    "Eusebio Gardella",
    "Hannes Thiel"
  ],
  "comment": "46 pages",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "For Banach spaces X and Y, we establish a natural bijection between preduals of Y and preduals of L(X,Y) that respect the right L(X)-module structure. If X is reflexive, it follows that there is a unique predual making L(X) into a dual Banach algebra. This removes the condition that X have the approximation property in a result of Daws. We further establish a natural bijection between projections that complement Y in its bidual and projections that complement L(X,Y) in its bidual as a right L(X)-module. It follows that Y is complemented in its bidual if and only if L(X,Y) is complemented in its bidual (either as a module or as a Banach space).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-17T12:40:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47L05",
      "47L10",
      "47L45",
      "46B10",
      "46B20"
    ],
    "keywords": [
      "bounded linear operators",
      "natural bijection",
      "complementation",
      "banach space",
      "dual banach algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}