Unconditionally saturated Banach space with the scalar-plus-compact property

Abstract

We construct a Bourgain-Delbaen ${\mathcal{L}}_{\infty }$-space ${\mathfrak{X}}_{Kus}$ with strongly heterogenous structure: any bounded operator on ${\mathfrak{X}}_{Kus}$ is a compact perturbation of a multiple of the identity, whereas the space ${\mathfrak{X}}_{Kus}$ is saturated with unconditional basic sequences.

The result about tightness removed,notation clarified and corrected, clarifying comments added, Journal of Functional Analysis, 2017

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