The famous Gowers tree space is the first example of a space not containing $c_0$, $\ell _1$ or a reflexive subspace. We present a space with a similar construction and prove that it is hereditarily indecomposable (HI) and has $\ell _2$ as a quotient space. Furthermore, we show that every bounded linear operator on it is of the form $\lambda I+W$ where $W$ is a weakly compact (hence strictly singular) operator.
Keywords:
famous gowers tree space first example space containing ell reflexive subspace present space similar construction prove hereditarily indecomposable has ell quotient space furthermore every bounded linear operator of form lambda where weakly compact hence strictly singular operator
Affiliations des auteurs :
Giorgos Petsoulas
1
;
Theocharis Raikoftsalis
1
1
Department of Mathematics Faculty of Applied Sciences National Technical University of Athens Zografou Campus 157 80, Athens, Greece
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author = {Giorgos Petsoulas and Theocharis Raikoftsalis},
title = {A {Gowers} tree like space and the space of its
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Giorgos Petsoulas; Theocharis Raikoftsalis. A Gowers tree like space and the space of its
bounded linear operators. Studia Mathematica, Tome 190 (2009) no. 3, pp. 233-281. doi: 10.4064/sm190-3-2
