The strong Nakano property in Banach lattices

Youssef Azouzi; Asma Ben Rjeb; Pedro Tradacete

paper

The strong Nakano property in Banach lattices

arXiv:2401.15629

Abstract

We study the strong Nakano property in Banach lattices with a special focus on free Banach lattices. We show that for every finite dimensional Banach space $E$ , the free Banach lattice $F B L [E]$ has the strong Nakano property with a constant independent of the dimension. It is also shown that if $F B L [E]$ has the strong Nakano property, then $E$ cannot contain subspaces isomorphic to neither $c_{0}$ nor $L_{1}$ .

21 pages