An Indecomposable and unconditionally saturated Banach space

Abstract

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.

25 pages, Dedicated to Professor Aleksander Pełczyński on the occasion of his 70th birthday

References in corpus (1)

• An arbitrarily distortable Banach space