# Hereditarily indecomposable, separable L infty spaces with ell 1 dual having few operators, but not very few operators - Mathematics > Functional Analysis

Hereditarily indecomposable, separable L infty spaces with ell 1 dual having few operators, but not very few operators - Mathematics > Functional Analysis - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: Given a natural number $k \geq 2$, we construct a hereditarilyindecomposable, $\mathscr{L} {\infty}$ space, $X k$ with dual isomorphic to$\ell 1$. We exhibit a non-compact, strictly singular operator $S$ on $X k$,with the property that $S^k = 0$ and $S^j 0 \leq j \leq k-1$ is not a compactperturbation of any linear combination of $S^l, l eq j$. Moreover, everybounded linear operator on this space has the form $\sum {i=0}^{k-1} \lambda iS^i +K$ where the $\lambda i$ are scalars and $K$ is compact. In particular,this construction answers a question of Argyros and Haydon -A hereditarilyindecomposable space that solves the scalar-plus-compact problem-.

Autor: Matthew Tarbard

Fuente: https://arxiv.org/