A class of Banach spaces with few non strictly singular operators

S. A. Argyros, J. Lopez-Abad, S. Todorcevic

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}_…