{
  "id": "1804.01372",
  "version": "v1",
  "published": "2018-04-04T12:43:31.000Z",
  "updated": "2018-04-04T12:43:31.000Z",
  "title": "Subsymmetric weak$^*$ Schauder bases and factorization of the identity",
  "authors": [
    "Richard Lechner"
  ],
  "comment": "16 pages, 1 figure",
  "doi": "10.4064/sm180404-29-9",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X^*$ denote a Banach space with a subsymmetric weak$^*$ Schauder basis satisfying condition~\\eqref{eq:condition-c}. We show that for any operator $T : X^*\\to X^*$, either $T(X^*)$ or $(I-T)(X^*)$ contains a subspace that is isomorphic to $X^*$ and complemented in $X^*$. Moreover, we prove that $\\ell^p(X^*)$, $1\\leq p \\leq \\infty$ is primary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-04T12:43:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B25",
      "46B26"
    ],
    "keywords": [
      "subsymmetric weak",
      "factorization",
      "banach space",
      "schauder basis satisfying"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}