This is an announcement for the paper “An Indecomposable and unconditionally saturated Banach space” by Spiros A. Argyroshttps://arxiv.org/find/math/1/au:+Argyros_S/0/1/0/all/0/1, A. Manoussakishttps://arxiv.org/find/math/1/au:+Manoussakis_A/0/1/0/all/0/1.

Abstract: We construct an indecomposable reflexive Banach space $\mathcal{X}_{ius}$ such that every infinite dimensional closed subspace contains an unconditional basic sequence. We also show that every operator $T\in B(\mathcal{X}_{ius})$ is of the form $\lambda I + S$ with $S$ a strictly singular operator.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.06509