Positions in $\ell_1$

Castillo, Jesús M. F.; Simões, Marilda A.

doi:10.15352/bjma/09-4-20

Cited by 2 publications

(1 citation statement)

References 14 publications

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“…Castillo, we do not known either. See [10] for the available information on twisted sums of ℓ 1 and c 0 and observe that our results do not solve any of the problems stated or suggested at the end of that paper.…”

Section: An Extension Of C 0 By ℓ 1 (Explicit Content)contrasting

confidence: 59%

When Kalton and Peck met Fourier

Sánchez¹,

Salguero-Alarcón²

2023

Annales De l'Institut Fourier

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The paper studies short exact sequences of Banach modules over the convolution algebra L 1 = L 1 (G), where G is a compact abelian group. The main tool is the notion of a nonlinear centralizer, which in combination with the Fourier transform, is used to produce sequences of L 1 -modules 0 → Lq → Z → Lp → 0 that are nontrivial as long as the general theory allows it, namely forConcrete examples are worked in detail for the circle group, with applications to the Hardy classes, and the Cantor group.Résumé. -L'article étudie des suites exactes courtes de modules de Banach sur l'algèbre de convolution L 1 = L 1 (G), où G est un groupe abélien compact. L'outil principal est la notion de centralisateur non linéaire, qui, en combinaison avec la transformée de Fourier, est utilisée pour produire des suites exactes de L 1 -modules de la forme 0 → Lq → Z → Lp → 0 qui sont non triviales tant que la théorie générale le permet, à savoir pour p ∈ (1, ∞], q ∈ [1, ∞). Des exemples concrets sont détaillés pour le groupe du cercle, avec des applications aux classes de Hardy, et le groupe de Cantor.

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Section: An Extension Of C 0 By ℓ 1 (Explicit Content)contrasting

confidence: 59%