A class of Banach spaces with few non strictly singular operators

Details A class of Banach spaces with few non strictly singular operators A class of Banach spaces with few non strictly singular operators

2003-12-31

arxiv.org/abs/math/0312522v2

Mathematics

Functional Analysis

52 pages, 1 figure

Scientific paper

We construct a family $(\mathcal{X}_\al)_{\al\le \omega_1}$ 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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