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.
Citation
Irene Deliyanni. Antonis Manoussakis. "Asymptotic $l\sb p$ hereditarily indecomposable Banach spaces." Illinois J. Math. 51 (3) 767 - 803, Fall 2007. https://doi.org/10.1215/ijm/1258131102
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