A class of Banach spaces with no unconditional basic sequence

Abstract

We give a construction of a reflexive Banach space X ω 1 with a transfinite basis of length ω 1 and with no unconditional basic sequence. In addition every bounded operator from a subspace of X ω 1 into the space X ω 1 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).