An Indecomposable and unconditionally saturated Banach space

@inproceedings{Argyros2003AnIA,
  title={An Indecomposable and unconditionally saturated Banach space},
  author={Spiros A. Argyros and Antonis Manoussakis},
  year={2003}
}
We construct an indecomposable reflexive Banach space $X_{ius}$ such that every infinite dimensional closed subspace contains an unconditional basic sequence. We also show that every operator $T\in \mathcal{B}(X_{ius})$ is of the form $\lambda I+S$ with $S$ a strictly singular operator.