{
  "id": "math/9610215",
  "version": "v1",
  "published": "1996-10-17T00:00:00.000Z",
  "updated": "1996-10-17T00:00:00.000Z",
  "title": "Operators on $C(ω^α)$ which do not preserve $C(ω^α)$",
  "authors": [
    "Dale E. Alspach"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "It is shown that if $\\alpha ,\\zeta $ are ordinals such that $1\\leq \\zeta <\\alpha <\\zeta \\omega ,$ then there is an operator from $C(\\omega ^{\\omega ^\\alpha })$ onto itself such that if $Y$ is a subspace of $C(\\omega ^{\\omega ^\\alpha })$ which is isomorphic to $C(\\omega ^{\\omega ^\\alpha })$ $,$ then the operator is not an isomorphism on $Y.$ This contrasts with a result of J. Bourgain that implies that there are uncountably many ordinals $\\alpha $ for which any operator from $C(\\omega ^{\\omega ^\\alpha })$ onto itself there is a subspace of $C(\\omega ^{\\omega ^\\alpha })$ which is isomorphic to $% C(\\omega ^{\\omega ^\\alpha })$ on which the operator is an isomorphism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-10-17T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B03"
    ],
    "keywords": [
      "isomorphic",
      "isomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1996math.....10215A"
    }
  }
}