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.
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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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