The famous Gowers tree space is the first example of a space not containing c₀, ℓ₁ or a reflexive subspace. We present a space with a similar construction and prove that it is hereditarily indecomposable (HI) and has ℓ₂ as a quotient space. Furthermore, we show that every bounded linear operator on it is of the form λI + W where W is a weakly compact (hence strictly singular) operator.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm190-3-2,
author = {Giorgos Petsoulas and Theocharis Raikoftsalis},
title = {A Gowers tree like space and the space of its bounded linear operators},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {233-281},
zbl = {1167.46007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm190-3-2}
}
Giorgos Petsoulas; Theocharis Raikoftsalis. A Gowers tree like space and the space of its bounded linear operators. Studia Mathematica, Tome 192 (2009) pp. 233-281. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm190-3-2/