A class of Banach spaces with no unconditional basic sequence |
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| Authors: | Spiros A Argyros Jordi Lopez-Abad Stevo Todorcevic |
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| Institution: | 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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| 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. To cite this article: S.A. Argyros et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003). |
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