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A class of Banach spaces with few non strictly singular operators

S. A. Argyros·J. Lopez-Abad·S. Todorcevic
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Abstract

We construct a family $(\mathcal{X}_\al)_{\al\le ω_1}$ of reflexive Banach spaces with long transfinite bases but with no unconditional basic sequences. In our spaces $\mathcal{X}_\al$ every bounded operator $T$ is split into its diagonal part $D_T$ and its strictly singular part $S_T$.

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BibTeXRIS

S. A. Argyros, J. Lopez-Abad, S. Todorcevic. 2004-10-27. A class of Banach spaces with few non strictly singular operators. https://arxiv.org/abs/math/0312522

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