{
  "id": "1903.01761",
  "version": "v1",
  "published": "2019-03-05T10:39:55.000Z",
  "updated": "2019-03-05T10:39:55.000Z",
  "title": "Daugavet property in tensor product spaces",
  "authors": [
    "Abraham Rueda Zoca",
    "Pedro Tradacete",
    "Ignacio Villanueva"
  ],
  "comment": "21 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the Daugavet property in tensor products of Banach spaces. We show that $L_1(\\mu)\\widehat{\\otimes}_\\varepsilon L_1(\\nu)$ has the Daugavet property when $\\mu$ and $\\nu$ are purely non-atomic measures. Also, we show that $X\\widehat{\\otimes}_\\pi Y$ has the Daugavet property provided $X$ and $Y$ are $L_1$-preduals with the Daugavet property, in particular spaces of continuous functions with this property. With the same tecniques, we also obtain consequences about roughness in projective tensor products as well as the Daugavet property of projective symmetric tensor products.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-05T10:39:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "46B20",
      "46B28"
    ],
    "keywords": [
      "daugavet property",
      "tensor product spaces",
      "projective symmetric tensor products",
      "banach spaces",
      "purely non-atomic measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}