{
  "id": "1210.3332",
  "version": "v1",
  "published": "2012-10-11T19:22:29.000Z",
  "updated": "2012-10-11T19:22:29.000Z",
  "title": "On Pietsch measures for summing operators and dominated polynomials",
  "authors": [
    "Geraldo Botelho",
    "Daniel Pellegrino",
    "Pilar Rueda"
  ],
  "comment": "13 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We relate the injectivity of the canonical map from $C(B_{E'})$ to $L_p(\\mu)$, where $\\mu$ is a regular Borel probability measure on the closed unit ball $B_{E'}$ of the dual $E'$ of a Banach space $E$ endowed with the weak* topology, to the existence of injective $p$-summing linear operators/$p$-dominated homogeneous polynomials defined on $E$ having $\\mu$ as a Pietsch measure. As an application we fill the gap in the proofs of some results of concerning Pietsch-type factorization of dominated polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-11T19:22:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28C15",
      "46G25",
      "47B10",
      "47L22"
    ],
    "keywords": [
      "pietsch measure",
      "dominated polynomials",
      "summing operators",
      "regular borel probability measure",
      "closed unit ball"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.3332B"
    }
  }
}