no. 5
When Kalton and Peck met Fourier
[Quand Kalton et Peck ont rencontré Fourier]
Cabello Sánchez, Félix1 ; Salguero-Alarcón, Alberto1
1 Instituto de Matemáticas Universidad de Extremadura Avenida de Elvas 06071-Badajoz (Spain)
Annales de l'Institut Fourier, Tome 73 (2023) no. 5, pp. 1843-1883.

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→L q →Z→L p →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.

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→L q →Z→L p →0 that are nontrivial as long as the general theory allows it, namely for p∈(1,∞],q∈[1,∞). Concrete examples are worked in detail for the circle group, with applications to the Hardy classes, and the Cantor group.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3562
Classification : 43A15, 43A20, 43A25, 46M18
Keywords: Short exact sequence, Banach module, Convolution algebra, Fourier transform, Nonlinear centralizer, Riesz product.
Mot clés : Suite exacte courte, Module de Banach, Algèbre de convolution, Transformée de Fourier, Centralisateur non linéaire, Produit de Riesz.
Cabello Sánchez, Félix 1 ; Salguero-Alarcón, Alberto 1

1 Instituto de Matemáticas Universidad de Extremadura Avenida de Elvas 06071-Badajoz (Spain)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Cabello Sánchez, Félix; Salguero-Alarcón, Alberto. When Kalton and Peck met Fourier. Annales de l'Institut Fourier, Tome 73 (2023) no. 5, pp. 1843-1883. doi : 10.5802/aif.3562. https://aif.centre-mersenne.org/articles/10.5802/aif.3562/

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