This is an announcement for the paper “The free Banach lattice generated by a Banach space” by Antonio Aviléshttps://arxiv.org/find/math/1/au:+Aviles_A/0/1/0/all/0/1, José Rodríguezhttps://arxiv.org/find/math/1/au:+Rodriguez_J/0/1/0/all/0/1, Pedro Tradacetehttps://arxiv.org/find/math/1/au:+Tradacete_P/0/1/0/all/0/1.
Abstract: The free Banach lattice over a Banach space is introduced and analyzed. This generalizes the concept of free Banach lattice over a set of generators, and allows us to study the Nakano property and the density character of non-degenerate intervals on these spaces, answering some recent questions of B. de Pagter and A.W. Wickstead. Moreover, an example of a Banach lattice which is weakly compactly generated as a lattice but not as a Banach space is exhibited, thus answering a question of J. Diestel.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1706.08147