A Godefroy-Kalton principle for free Banach lattices
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 satisfies the lattice-lifting property if every lattice homomorphism to 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 -unconditional basis as well as free Banach lattices. The case of spaces will also be analyzed.
Keywords
Cite
@article{arxiv.2011.04639,
title = {A Godefroy-Kalton principle for free Banach lattices},
author = {Antonio Avilés and Gonzalo Martínez-Cervantes and José Rodríguez and Pedro Tradacete},
journal= {arXiv preprint arXiv:2011.04639},
year = {2020}
}