On the structure of Banach spaces with an unconditional basic sequence

Razvan Anisca. "On the structure of Banach spaces with an unconditional basic sequence." Studia Mathematica 182.1 (2007): 67-85. <http://eudml.org/doc/285140>.

@article{RazvanAnisca2007,
abstract = {For a Banach space X with an unconditional basic sequence, one of the following regular-irregular alternatives holds: either X contains a subspace isomorphic to ℓ₂, or X contains a subspace which has an unconditional finite-dimensional decomposition, but does not admit such a decomposition with a uniform bound for the dimensions of the decomposition. This result can be viewed in the context of Gowers' dichotomy theorem.},
author = {Razvan Anisca},
journal = {Studia Mathematica},
keywords = {unconditional basis; unconditional decomposition; local unconditional structure},
language = {eng},
number = {1},
pages = {67-85},
title = {On the structure of Banach spaces with an unconditional basic sequence},
url = {http://eudml.org/doc/285140},
volume = {182},
year = {2007},
}

TY - JOUR
AU - Razvan Anisca
TI - On the structure of Banach spaces with an unconditional basic sequence
JO - Studia Mathematica
PY - 2007
VL - 182
IS - 1
SP - 67
EP - 85
AB - For a Banach space X with an unconditional basic sequence, one of the following regular-irregular alternatives holds: either X contains a subspace isomorphic to ℓ₂, or X contains a subspace which has an unconditional finite-dimensional decomposition, but does not admit such a decomposition with a uniform bound for the dimensions of the decomposition. This result can be viewed in the context of Gowers' dichotomy theorem.
LA - eng
KW - unconditional basis; unconditional decomposition; local unconditional structure
UR - http://eudml.org/doc/285140
ER -