The paper studies short exact sequences of Banach modules over the convolution algebra , where 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 -modules that are nontrivial as long as the general theory allows it, namely for . Concrete examples are worked in detail for the circle group, with applications to the Hardy classes, and the Cantor group.
L’article étudie des suites exactes courtes de modules de Banach sur l’algèbre de convolution , où 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 -modules de la forme qui sont non triviales tant que la théorie générale le permet, à savoir pour . Des exemples concrets sont détaillés pour le groupe du cercle, avec des applications aux classes de Hardy, et le groupe de Cantor.
Revised:
Accepted:
Published online:
Keywords: Short exact sequence, Banach module, Convolution algebra, Fourier transform, Nonlinear centralizer, Riesz product.
Mots-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

@article{AIF_2023__73_5_1843_0, author = {Cabello S\'anchez, F\'elix and Salguero-Alarc\'on, Alberto}, title = {When {Kalton} and {Peck} met {Fourier}}, journal = {Annales de l'Institut Fourier}, pages = {1843--1883}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {73}, number = {5}, year = {2023}, doi = {10.5802/aif.3562}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3562/} }
TY - JOUR AU - Cabello Sánchez, Félix AU - Salguero-Alarcón, Alberto TI - When Kalton and Peck met Fourier JO - Annales de l'Institut Fourier PY - 2023 SP - 1843 EP - 1883 VL - 73 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3562/ DO - 10.5802/aif.3562 LA - en ID - AIF_2023__73_5_1843_0 ER -
%0 Journal Article %A Cabello Sánchez, Félix %A Salguero-Alarcón, Alberto %T When Kalton and Peck met Fourier %J Annales de l'Institut Fourier %D 2023 %P 1843-1883 %V 73 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3562/ %R 10.5802/aif.3562 %G en %F AIF_2023__73_5_1843_0
Cabello Sánchez, Félix; Salguero-Alarcón, Alberto. When Kalton and Peck met Fourier. Annales de l'Institut Fourier, Volume 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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