Duality, reflexivity and atomic decompositions in Banach spaces

Daniel Carando, and Silvia Lassalle. "Duality, reflexivity and atomic decompositions in Banach spaces." Studia Mathematica 191.1 (2009): 67-80. <http://eudml.org/doc/284393>.

@article{DanielCarando2009,
abstract = {We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of "shrinking" and "boundedly complete" Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. We also characterize the reflexivity of a Banach space in terms of properties of its atomic decompositions.},
author = {Daniel Carando, Silvia Lassalle},
journal = {Studia Mathematica},
keywords = {atomic decompositions; duality; reflexivity; Banach frames},
language = {eng},
number = {1},
pages = {67-80},
title = {Duality, reflexivity and atomic decompositions in Banach spaces},
url = {http://eudml.org/doc/284393},
volume = {191},
year = {2009},
}

TY - JOUR
AU - Daniel Carando
AU - Silvia Lassalle
TI - Duality, reflexivity and atomic decompositions in Banach spaces
JO - Studia Mathematica
PY - 2009
VL - 191
IS - 1
SP - 67
EP - 80
AB - We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of "shrinking" and "boundedly complete" Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. We also characterize the reflexivity of a Banach space in terms of properties of its atomic decompositions.
LA - eng
KW - atomic decompositions; duality; reflexivity; Banach frames
UR - http://eudml.org/doc/284393
ER -