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- W4287992030 abstract "We construct for each $0<ple 1$ an infinite collection of subspaces of $ell_p$ that extend the example from [J. Lindenstrauss, On a certain subspace of $ell_{1}$, Bull. Acad. Polon. Sci. S'er. Sci. Math. Astronom. Phys. 12 (1964), 539-542] of a subspace of $ell_{1}$ with no unconditional basis. The structure of this new class of $p$-Banach spaces is analyzed and some applications to the general theory of $mathcal{L}_{p}$-spaces for $0<p<1$ are provided. The introduction of these spaces serves the purpose to develop the theory of conditional quasi-greedy bases in $p$-Banach spaces for $p<1$. Among the topics we consider are the existence of infinitely many conditional quasi-greedy bases in the spaces $ell_{p}$ for $ple 1$ and the careful examination of the conditionality constants of the natural basis of these spaces." @default.
- W4287992030 created "2022-07-26" @default.
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- W4287992030 date "2019-12-18" @default.
- W4287992030 modified "2023-09-24" @default.
- W4287992030 title "On certain subspaces of $ell_p$ for $0<ple 1$ and their applications to conditional quasi-greedy bases in $p$-Banach spaces" @default.
- W4287992030 doi "https://doi.org/10.48550/arxiv.1912.08449" @default.
- W4287992030 hasPublicationYear "2019" @default.
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