An Indecomposable and unconditionally saturated Banach space
  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. 
Spiros A. Argyros, A. Manoussakis
math.FA