{
  "id": "2410.12666",
  "version": "v1",
  "published": "2024-10-16T15:29:32.000Z",
  "updated": "2024-10-16T15:29:32.000Z",
  "title": "Closed ideals of operators on the Baernstein and Schreier spaces",
  "authors": [
    "Niels Jakob Laustsen",
    "James Smith"
  ],
  "comment": "28 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the lattice of closed ideals of bounded operators on two families of Banach spaces: the Baernstein spaces $B_p$ for $1<p<\\infty$ and the Schreier spaces $S_p$ for $1\\le p<\\infty$. Our main conclusion is that there are $2^{\\mathfrak{c}}$ many closed ideals that lie between the ideals of compact and strictly singular operators on each of these spaces, and also $2^{\\mathfrak{c}}$ many closed ideals that contain projections of infinite rank. Counterparts of results of Gasparis and Leung using a numerical index to distinguish the isomorphism types of subspaces spanned by subsequences of the unit vector basis for the higher-order Schreier spaces play a key role in the proofs, as does the Johnson-Schechtman technique for constructing $2^{\\mathfrak{c}}$ many closed ideals of operators on a Banach space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-16T15:29:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46H10",
      "47L10",
      "46B03",
      "46B45",
      "47L20"
    ],
    "keywords": [
      "closed ideals",
      "banach space",
      "higher-order schreier spaces play",
      "unit vector basis",
      "baernstein spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}