{
  "id": "math/9610213",
  "version": "v1",
  "published": "1996-10-14T00:00:00.000Z",
  "updated": "1996-10-14T00:00:00.000Z",
  "title": "A counterexample to a question of Haydon, Odell and Rosenthal",
  "authors": [
    "George Androulakis"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We give an example of a compact metric space $K$, an open dense subset $U$ of $K$, and a sequence $(f_n)$ in $C(K)$ which is pointwise convergent to a non-continuous function on $K$, such that for every $u \\in U$ there exists $n \\in \\N$ with $f_n(u)=f_m(u)$ for all $m \\geq n$, yet $(f_n)$ is equivalent to the unit vector basis of the James quasi-reflexive space of order 1. Thus $c_0$ does not embed isomorphically in the closed linear span $[f_n]$ of $(f_n)$. This answers in negative a question asked by H. Haydon, E. Odell and H. Rosenthal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-10-14T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B25"
    ],
    "keywords": [
      "counterexample",
      "compact metric space",
      "open dense subset",
      "unit vector basis",
      "james quasi-reflexive space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1996math.....10213A"
    }
  }
}