Complete latticeability in vector‐valued sequence spaces

Geraldo Botelho and José Lucas P. Luiz

Mathematische Nachrichten, 2023, vol. 296, issue 2, 523-533

Abstract: Using a technique due to Jiménez–Rodríguez, first we 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 λπ(E)∖λs(E)$\lambda _\pi (E) \setminus \lambda _s(E)$, which implies the complete latticeability of (ℓp⊗̂|π|E)∖(ℓp⊗̂πE)$(\ell _p\widehat{\otimes }_{|\pi |}E)\setminus (\ell _p\widehat{\otimes }_{\pi }E)$, where E is a Banach lattice and 1

Date: 2023
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