{
  "id": "1512.08741",
  "version": "v1",
  "published": "2015-12-29T18:10:41.000Z",
  "updated": "2015-12-29T18:10:41.000Z",
  "title": "Ideal structures in vector-valued polynomial spaces",
  "authors": [
    "Verónica Dimant",
    "Silvia Lassalle",
    "Ángeles Prieto"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper is concerned with the study of geometric structures in spaces of polynomials. More precisely, we discuss for $E$ and $F$ Banach spaces, whether the class of weakly continuous on bounded sets $n$-homogeneous polynomials, $\\mathcal P_w(^n E, F)$, is an HB-subspace or an $M(1,C)$-ideal in the space of continuous $n$-homogeneous polynomials, $\\mathcal P(^n E, F)$. We establish sufficient conditions under which the problem can be positively solved. Some examples are given. We also study when some ideal structures pass from $\\mathcal P_w(^n E, F)$ as an ideal in $\\mathcal P(^n E, F)$ to the range space $F$ as an ideal in its bidual $F^{**}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-29T18:10:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46G25",
      "47H60",
      "46B04",
      "47L22"
    ],
    "keywords": [
      "vector-valued polynomial spaces",
      "homogeneous polynomials",
      "ideal structures pass",
      "geometric structures",
      "banach spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151208741D"
    }
  }
}