Authors: Argyros, Spiros
Lopez-Abad, Jordi
Todorčević, Stevo 
Title: A class of Banach spaces with no unconditional basic sequence
Other Titles: Une classe d'espace de Banach sans suite basique inconditionnelle
Journal: Comptes Rendus Mathematique
Volume: 337
Issue: 1
First page: 43
Last page: 48
Issue Date: 1-Jul-2003
Rank: M23
ISSN: 1631-073X
DOI: 10.1016/S1631-073X(03)00272-3
Abstract: 
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.
Publisher: Elsevier

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