Comptes Rendus
no. 1
Functional Analysis
A class of Banach spaces with no unconditional basic sequence
[Une classe d'espace de Banach sans suite basique inconditionnelle]

Présenté par : Michel Talagrand

Spiros A. Argyros1 ; Jordi Lopez-Abad2 ; Stevo Todorcevic3
1 Department of Mathematics, National Technical University of Athens, Zogratou Campus, 15780 Athens, Greece
2 Équipe de logique mathématique, Université Paris VII, 2, place Jussieu, 75251 Paris cedex, France
3 CNRS–Université Paris VII, 2, place Jussieu, 75251 Paris cedex, France
Comptes Rendus. Mathématique, Volume 337 (2003) no. 1, pp. 43-48.

Nous construisons un espace de Banach réflexif Xω1 ayant une base transfinie de longueur ω1 et n'admettant aucune suite basique inconditionnelle. De plus, tout opérateur borné d'un sous-espace de Xω1 dans cet espace est somme d'un opérateur diagonal très simple et d'un opérateur strictement singulier.

We give a construction of a reflexive Banach space Xω1 with a transfinite basis of length ω1 and with no unconditional basic sequence. In addition every bounded operator from a subspace of Xω1 into the space Xω1 is a sum of a simple diagonal operator and a strictly singular one.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00272-3
Spiros A. Argyros 1 ; Jordi Lopez-Abad 2 ; Stevo Todorcevic 3

1 Department of Mathematics, National Technical University of Athens, Zogratou Campus, 15780 Athens, Greece
2 Équipe de logique mathématique, Université Paris VII, 2, place Jussieu, 75251 Paris cedex, France
3 CNRS–Université Paris VII, 2, place Jussieu, 75251 Paris cedex, France 
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     title = {A class of {Banach} spaces with no unconditional basic sequence},
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Spiros A. Argyros; Jordi Lopez-Abad; Stevo Todorcevic. A class of Banach spaces with no unconditional basic sequence. Comptes Rendus. Mathématique, Volume 337 (2003) no. 1, pp. 43-48. doi : 10.1016/S1631-073X(03)00272-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00272-3/

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