{
  "id": "2404.01419",
  "version": "v1",
  "published": "2024-04-01T18:53:51.000Z",
  "updated": "2024-04-01T18:53:51.000Z",
  "title": "$2$-rotund norms for unconditional and symmetric sequence spaces",
  "authors": [
    "Stephen Dilworth",
    "Denka Kutzarova",
    "Pavlos Motakis"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "A reflexive Banach space with an unconditional basis admits an equivalent $1$-unconditional $2R$ norm and embeds into a reflexive space with a $1$-symmetric $2R$ norm. Partial results on $1$-symmetric $2R$ renormings of spaces with a symmetric basis are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-01T18:53:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric sequence spaces",
      "rotund norms",
      "unconditional basis admits",
      "partial results",
      "reflexive banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}