A Banach space dichotomy theorem for quotients of subspaces

@article{ValentinFerenczi2007,
abstract = {A Banach space X with a Schauder basis is defined to have the restricted quotient hereditarily indecomposable property if X/Y is hereditarily indecomposable for any infinite-codimensional subspace Y with a successive finite-dimensional decomposition on the basis of X. The following dichotomy theorem is proved: any infinite-dimensional Banach space contains a quotient of a subspace which either has an unconditional basis, or has the restricted quotient hereditarily indecomposable property.},
author = {Valentin Ferenczi},
journal = {Studia Mathematica},
keywords = {Gowers' dichotomy theorem; unconditional basis; hereditarily indecomposable; quotient of subspace; combinatorial forcing; restricted quotient H.I.},
language = {eng},
number = {2},
pages = {111-131},
title = {A Banach space dichotomy theorem for quotients of subspaces},
url = {http://eudml.org/doc/284970},
volume = {180},
year = {2007},
}

TY - JOUR
AU - Valentin Ferenczi
TI - A Banach space dichotomy theorem for quotients of subspaces
JO - Studia Mathematica
PY - 2007
VL - 180
IS - 2
SP - 111
EP - 131
AB - A Banach space X with a Schauder basis is defined to have the restricted quotient hereditarily indecomposable property if X/Y is hereditarily indecomposable for any infinite-codimensional subspace Y with a successive finite-dimensional decomposition on the basis of X. The following dichotomy theorem is proved: any infinite-dimensional Banach space contains a quotient of a subspace which either has an unconditional basis, or has the restricted quotient hereditarily indecomposable property.
LA - eng
KW - Gowers' dichotomy theorem; unconditional basis; hereditarily indecomposable; quotient of subspace; combinatorial forcing; restricted quotient H.I.
UR - http://eudml.org/doc/284970
ER -