The free Banach lattice generated by a Banach space
Functional Analysis
2017-06-27 v1
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.
Keywords
Cite
@article{arxiv.1706.08147,
title = {The free Banach lattice generated by a Banach space},
author = {Antonio Avilés and José Rodríguez and Pedro Tradacete},
journal= {arXiv preprint arXiv:1706.08147},
year = {2017}
}