An Indecomposable and unconditionally saturated Banach space

Published 21 Sep 2016 in math.FA | (1609.06509v1)

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.

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