A class of Banach spaces with no unconditional basic sequence

Spiros A. Argyros; Jordi Lopez-Abad; Stevo Todorcevic

doi:10.1016/S1631-073X(03)00272-3

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. 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

Comptes Rendus. Mathématique, Volume 337 (2003) no. 1, pp. 43-48.

Résumé
Abstract

Nous construisons un espace de Banach réflexif X_ω₁ ayant une base transfinie de longueur ω₁ et n'admettant aucune suite basique inconditionnelle. De plus, tout opérateur borné d'un sous-espace de X_ω₁ 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 X_ω₁ with a transfinite basis of length ω₁ and with no unconditional basic sequence. In addition every bounded operator from a subspace of X_ω₁ into the space X_ω₁ is a sum of a simple diagonal operator and a strictly singular one.

Reçu le : 2003-05-26
Accepté le : 2003-05-27
Publié le : 2003-06-26

DOI : 10.1016/S1631-073X(03)00272-3

Affiliations des auteurs :

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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     author = {Spiros A. Argyros and Jordi Lopez-Abad and Stevo Todorcevic},
     title = {A class of {Banach} spaces with no unconditional basic sequence},
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     pages = {43--48},
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     number = {1},
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     doi = {10.1016/S1631-073X(03)00272-3},
     language = {en},
}

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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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