{
  "id": "math/9605213",
  "version": "v1",
  "published": "1996-05-09T00:00:00.000Z",
  "updated": "1996-05-09T00:00:00.000Z",
  "title": "On nicely smooth Banach spaces",
  "authors": [
    "Pradipta Bandyopadhyay",
    "Sudeshna Basu"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this work, we obtain some necessary and some sufficient conditions for a space to be nicely smooth, and show that they are equivalent for separable or Asplund spaces. We obtain a sufficient condition for the Ball Generated Property (BGP), and conclude that Property $(II)$ implies the BGP, which, in turn, implies the space is nicely smooth. We show that the class of nicely smooth spaces is stable under $c_o$ and $\\ell_p$ sums and also under finite $\\ell_1$ sums; that being nicely smooth is not a three space property; and that the Bochner $L_p$ spaces are nicely smooth if and only if $X$ is both nicely smooth and Asplund. A striking result obtained is that every equivalent renorming of a space is nicely smooth if and only if it is reflexive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-05-09T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46B22"
    ],
    "keywords": [
      "nicely smooth banach spaces",
      "sufficient condition",
      "equivalent",
      "asplund spaces",
      "space property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1996math......5213B"
    }
  }
}