A hereditarily indecomposable L_\infty-space that solves the scalar-plus-compact problem

Spiros A Argyros, Richard G Haydon

We construct a hereditarily indecomposable Banach space with dual isomorphic to ${\ell }_1$. Every bounded linear operator on this space has the form $\lambda I+K$ with $\lambda$ a scalar and $K$…