A hereditarily ℓ₁ subspace of 𝐿₁ without the Schur property
Copyright policy )A hereditarily ℓ₁ subspace of 𝐿₁ without the Schur property
Let ∞ > p 1 > p 2 > ⋯ > 1 \infty > p_1 > p_2 > \cdots > 1 . We construct an easily determined 1 1 -symmetric basic sequence in ( ∑ n = 1 ∞ ⊕ ℓ p n ) 1 \Bigl ( \sum \limits _{n=1}^{\infty } \oplus \ell _{p_n} \Bigr )_1 , which spans a hereditarily ℓ 1 \ell _1 subspace without the Schur property. An immediate consequence is the existence of hereditarily ℓ 1 \ell _1 subspaces of L 1 L_1 without the Schur property.
- Chernivtsi National University Ukraine
Isomorphic theory (including renorming) of Banach spaces, hereditarily-\(\ell_1\) Banach space, Classical Banach spaces in the general theory, Schur property
Isomorphic theory (including renorming) of Banach spaces, hereditarily-\(\ell_1\) Banach space, Classical Banach spaces in the general theory, Schur property
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