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Comptes Rendus Mathématique
Volume 337, n° 1
pages 43-48 (juillet 2003)
Doi : 10.1016/S1631-073X(03)00272-3
Received : 26 May 2003 ;  accepted : 27 May 2003
A class of Banach spaces with no unconditional basic sequence

Spiros A.  Argyros a ,  Jordi  Lopez-Abad b ,  Stevo  Todorcevic c
aDepartment of Mathematics, National Technical University of Athens, Zogratou Campus, 15780 Athens, Greece 
bÉquipe de logique mathématique, Université Paris VII, 2, place Jussieu, 75251 Paris cedex, France 
cCNRS-Université Paris VII, 2, place Jussieu, 75251 Paris cedex, France 


We give a construction of a reflexive Banach space   with a transfinite basis of length   and with no unconditional basic sequence. In addition every bounded operator from a subspace of   into the space   is a sum of a simple diagonal operator and a strictly singular one. To cite this article: S.A. Argyros et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).


Nous construisons un espace de Banach réflexif   ayant une base transfinie de longueur   et n'admettant aucune suite basique inconditionnelle. De plus, tout opérateur borné d'un sous-espace de   dans cet espace est somme d'un opérateur diagonal très simple et d'un opérateur strictement singulier. Pour citer cet article : S.A. Argyros et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).

© 2003  Académie des sciences@@#104156@@

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