{
  "id": "1608.06926",
  "version": "v1",
  "published": "2016-08-24T19:40:04.000Z",
  "updated": "2016-08-24T19:40:04.000Z",
  "title": "Spaces of ?sigma(p)-nuclear linear and multilinear operators and their duals",
  "authors": [
    "Geraldo Botelho",
    "Ximena Mujica"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The theory of ?tau-summing and sigma?-nuclear linear operators on Banach spaces was developed by Pietsch [12, Chapter 23]. Extending the linear case to the range p > 1 and generalizing all cases to the multilinear setting, in this paper we introduce the concept of ?sigma(p)-nuclear linear and multilinear operators. In order to develop the duality theory for the spaces of such operators, we introduce the concept of quasi-tau(p)-summing linear/multilinear operators and prove Pietsch-type domination theorems for such operators. The main result of the paper shows that, under usual conditions, linear functionals on the space of sigma?(p)-nuclear n-linear operators are represented, via the Borel transform, by quasi-tau(p)-summing n-linear operators. As far as we know, this result is new even in the linear case n = 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-24T19:40:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47L22",
      "46G25",
      "47B10",
      "46A20"
    ],
    "keywords": [
      "multilinear operators",
      "linear case",
      "n-linear operators",
      "pietsch-type domination theorems",
      "borel transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}