Salvato in:
| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2410.16886 |
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Sommario:
- We show that if $p>1$ every subspace of $\ell_p(Γ)$ is an $\ell_p$-sum of separable subspaces of $\ell_p$, and we provide examples of subspaces of $\ell_p(Γ)$ for $0<p\leq 1$ that are not even isomorphic to any $\ell_p$-sum of separable spaces, notably the kernel of any quotient map $\ell_p(Γ)\to L_1(2^Γ)$ with $Γ$ uncountable. We involve the separable complementation property (SCP) and the separable extension property (SEP), showing that if $X$ is a Banach space of density character $\aleph_1$ with the SCP then the kernel of any quotient map $\ell_p(Γ)\to X$ is a complemented subspace of a space with the SCP and, consequently, has the SEP.