## Illinois Journal of Mathematics

### Asymptotic $l\sb p$ hereditarily indecomposable Banach spaces

#### Abstract

For every $1 < p < \infty$ we construct an asymptotic $\ell_{p}$ Banach space which is hereditarily indecomposable and such that its dual is asymptotic $\ell_{q}$ hereditarily indecomposable, where $q$ is the conjugate of $p$. We prove that $c_{0}$ is finitely representable in these spaces and that every bounded linear operator on these spaces is a strictly singular perturbation of a multiple of the identity.

#### Article information

Source
Illinois J. Math., Volume 51, Number 3 (2007), 767-803.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258131102

Digital Object Identifier
doi:10.1215/ijm/1258131102

Mathematical Reviews number (MathSciNet)
MR2379722

Zentralblatt MATH identifier
1160.46006

#### Citation

Deliyanni, Irene; Manoussakis, Antonis. Asymptotic $l\sb p$ hereditarily indecomposable Banach spaces. Illinois J. Math. 51 (2007), no. 3, 767--803. doi:10.1215/ijm/1258131102. https://projecteuclid.org/euclid.ijm/1258131102