{
  "id": "2012.09492",
  "version": "v1",
  "published": "2020-12-17T10:33:13.000Z",
  "updated": "2020-12-17T10:33:13.000Z",
  "title": "Stability of diametral diameter two properties",
  "authors": [
    "Johann Langemets",
    "Katriin Pirk"
  ],
  "comment": "14 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that the diametral diameter two properties are inherited by $F$-ideals (e.g., $M$-ideals). On the other hand, these properties are lifted from an $M$-ideal to the superspace under strong geometric assumptions. We also show that all of the diametral diameter two properties are stable under the formation of corresponding K\\\"othe-Bochner spaces (e.g., $L_p$-Bochner spaces). Finally, we investigate when the projective tensor product of two Banach spaces has some diametral diameter two property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-17T10:33:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "46B20",
      "46B22",
      "46B42"
    ],
    "keywords": [
      "diametral diameter",
      "strong geometric assumptions",
      "bochner spaces",
      "projective tensor product",
      "banach spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}