A hereditarily ℓ₁ subspace of 𝐿₁ without the Schur property

Popov, M.

doi:10.1090/S0002-9939-05-07758-0

A hereditarily $\ell _1$ subspace of $L_1$ without the Schur property
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Proc. Amer. Math. Soc. 133 (2005), 2023-2028 Request permission

Abstract:

Let $\infty > p_1 > p_2 > \cdots > 1$. We construct an easily determined $1$-symmetric basic sequence in $\Bigl ( \sum \limits _{n=1}^{\infty } \oplus \ell _{p_n} \Bigr )_1$, which spans a hereditarily $\ell _1$ subspace without the Schur property. An immediate consequence is the existence of hereditarily $\ell _1$ subspaces of $L_1$ without the Schur property.

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