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.
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.
Accepted:
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Spiros A. Argyros 1; Jordi Lopez-Abad 2; Stevo Todorcevic 3
@article{CRMATH_2003__337_1_43_0, author = {Spiros A. Argyros and Jordi Lopez-Abad and Stevo Todorcevic}, title = {A class of {Banach} spaces with no unconditional basic sequence}, journal = {Comptes Rendus. Math\'ematique}, pages = {43--48}, publisher = {Elsevier}, volume = {337}, number = {1}, year = {2003}, doi = {10.1016/S1631-073X(03)00272-3}, language = {en}, }
TY - JOUR AU - Spiros A. Argyros AU - Jordi Lopez-Abad AU - Stevo Todorcevic TI - A class of Banach spaces with no unconditional basic sequence JO - Comptes Rendus. Mathématique PY - 2003 SP - 43 EP - 48 VL - 337 IS - 1 PB - Elsevier DO - 10.1016/S1631-073X(03)00272-3 LA - en ID - CRMATH_2003__337_1_43_0 ER -
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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