A hereditarily indecomposable $ {\mathcal{L}_{\infty}} $-space that solves the scalar-plus-compact problem

Abstract

haydon result to say that an HI predual of 1 necessarily has the scalar-plus-compact property. We use, in an essential way, the specific structure of the BD construction, which embeds into our space some very explicit finite-dimensional -spaces. As well as the (now) classical machinery of HI constructions-a space of Schlumprecht type (cf. This allows us to introduce two additional classes of rapidly increasing sequences, and these in turn lead to the stronger result about operators.