A Godefroy-Kalton principle for free Banach lattices Articles uri icon


  • Aviles, Antonio
  • Martinez Cervantes, Gonzalo
  • Rodriguez, Jose

publication date

  • April 2022

start page

  • 433

end page

  • 458


  • 1


  • 247

International Standard Serial Number (ISSN)

  • 0021-2172

Electronic International Standard Serial Number (EISSN)

  • 1565-8511


  • 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.


  • Mathematics