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arXiv · 2004.01604

Complete latticeability in vector-valued sequence spaces

Geraldo Botelho·José Lucas P. Luiz
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Abstract

First we adjust a technique due to Jim\'enez-Rodr\'iguez 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 $(\ell_p\widehat{\otimes}_{|\pi|}E)\setminus(\ell_p\widehat{\otimes}_{\pi}E)$, where $E$ is a Banach lattice and $1 < p < \infty$.

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Geraldo Botelho, José Lucas P. Luiz. 2020-04-03. Complete latticeability in vector-valued sequence spaces. https://arxiv.org/abs/2004.01604

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