{
  "id": "1407.7848",
  "version": "v1",
  "published": "2014-07-29T19:53:19.000Z",
  "updated": "2014-07-29T19:53:19.000Z",
  "title": "On Banach spaces with the approximate hyperplane series property",
  "authors": [
    "Yun Sung Choi",
    "Sun Kwang Kim",
    "Han Ju Lee",
    "Miguel Martín"
  ],
  "comment": "12 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We present a sufficient condition for a Banach space to have the approximate hyperplane series property (AHSP) which actually covers all known examples. We use this property to get a stability result to vector-valued spaces of integrable functions. On the other hand, the study of a possible Bishop-Phelps-Bollob\\'as version of a classical result of V. Zizler leads to a new characterization of the AHSP for dual spaces in terms of $w^*$-continuous operators and other related results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-29T19:53:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46B04",
      "46B22"
    ],
    "keywords": [
      "approximate hyperplane series property",
      "banach space",
      "sufficient condition",
      "stability result",
      "bishop-phelps-bollobas version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.7848C"
    }
  }
}