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

Abstract

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 $K$ compact.

Cited by in corpus (4)

• Operator machines on directed graphs
• On typical properties of Hilbert space operators
• B(l^p) is never amenable
• More (\ell_r) saturated (\mathcal{L}_\infty) spaces