Complete latticeability in vector-valued sequence spaces

Abstract

First we adjust a technique due to Jiménez-Rodríguez to prove the complete latticeability of the set of disjoint non-norm null weakly null sequences and of the set of disjoint non-norm null regular-polynomially null sequences in Banach lattices. Then we apply the mother vector technique to prove the complete latticeability of ${\lambda }_{\pi }(E)\setminus {\lambda }_s(E)$, which implies the complete latticeability of $({\ell }_p{\hat{\otimes }}_{|\pi |}E)\setminus ({\ell }_p{\hat{\otimes }}_{\pi }E)$, where $E$ is a Banach lattice and $1<p<\infty$.

15 pages