{
  "id": "2011.04639",
  "version": "v1",
  "published": "2020-11-09T18:50:36.000Z",
  "updated": "2020-11-09T18:50:36.000Z",
  "title": "A Godefroy-Kalton principle for free Banach lattices",
  "authors": [
    "Antonio Avilés",
    "Gonzalo Martínez-Cervantes",
    "José Rodríguez",
    "Pedro Tradacete"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Motivated by the Lipschitz-lifting property of Banach spaces introduced by Godefroy and Kalton, we consider the lattice-lifting property, which is an analogous notion within the category of Banach lattices and lattice homomorphisms. Namely, a Banach lattice $X$ satisfies the lattice-lifting property if every lattice homomorphism to $X$ having a bounded linear right-inverse must have a lattice homomorphism right-inverse. In terms of free Banach lattices, this can be rephrased into the following question: which Banach lattices embed into the free Banach lattice which they generate as a lattice-complemented sublattice? We will provide necessary conditions for a Banach lattice to have the lattice-lifting property, and show that this property is shared by Banach spaces with a $1$-unconditional basis as well as free Banach lattices. The case of $C(K)$ spaces will also be analyzed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-09T18:50:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B42"
    ],
    "keywords": [
      "free banach lattice",
      "godefroy-kalton principle",
      "lattice-lifting property",
      "banach spaces",
      "lattice homomorphism right-inverse"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}