A Gowers tree like space and the space of its bounded linear operators

Giorgos Petsoulas, and Theocharis Raikoftsalis. "A Gowers tree like space and the space of its bounded linear operators." Studia Mathematica 190.3 (2009): 233-281. <http://eudml.org/doc/284826>.

@article{GiorgosPetsoulas2009,
abstract = {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.},
author = {Giorgos Petsoulas, Theocharis Raikoftsalis},
journal = {Studia Mathematica},
keywords = {hereditarily indecomposable Banach space; strictly singular operators; Gowers tree space; James tree space},
language = {eng},
number = {3},
pages = {233-281},
title = {A Gowers tree like space and the space of its bounded linear operators},
url = {http://eudml.org/doc/284826},
volume = {190},
year = {2009},
}

TY - JOUR
AU - Giorgos Petsoulas
AU - Theocharis Raikoftsalis
TI - A Gowers tree like space and the space of its bounded linear operators
JO - Studia Mathematica
PY - 2009
VL - 190
IS - 3
SP - 233
EP - 281
AB - 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.
LA - eng
KW - hereditarily indecomposable Banach space; strictly singular operators; Gowers tree space; James tree space
UR - http://eudml.org/doc/284826
ER -