This is an announcement for the paper “Unconditionally saturated Banach space with the scalar-plus-compact property” by Antonis Manoussakishttps://arxiv.org/find/math/1/au:+Manoussakis_A/0/1/0/all/0/1, Anna Pelczar-Barwaczhttps://arxiv.org/find/math/1/au:+Pelczar_Barwacz_A/0/1/0/all/0/1, Michał Świȩtekhttps://arxiv.org/find/math/1/au:+Swietek_M/0/1/0/all/0/1.
Abstract: We construct a Bourgain-Delbaen $\mathcal{L}_\infty$-space $\mathcal{X}_{kus}$ with strongly heterogenous structure: any bounded operator on $\mathcal{X}_{kus}$ is a compact perturbation of a multiple of the identity, whereas the space $\mathcal{X}_{kus}$ is saturated with unconditional basic sequences.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.06506