Dual spaces generated by the interior of the set of norm attaining functionals

Maria D. Acosta, Julio Becerra Guerrero, and Manuel Ruiz Galán. "Dual spaces generated by the interior of the set of norm attaining functionals." Studia Mathematica 149.2 (2002): 175-183. <http://eudml.org/doc/284476>.

@article{MariaD2002,
abstract = {We characterize some isomorphic properties of Banach spaces in terms of the set of norm attaining functionals. The main result states that a Banach space is reflexive as soon as it does not contain ℓ₁ and the dual unit ball is the w*-closure of the convex hull of elements contained in the "uniform" interior of the set of norm attaining functionals. By assuming a very weak isometric condition (lack of roughness) instead of not containing ℓ₁, we also obtain a similar result. As a consequence of the first result, a convex-transitive Banach space not containing ℓ₁ and such that the set of norm attaining functionals has nonempty interior is in fact superreflexive.},
author = {Maria D. Acosta, Julio Becerra Guerrero, Manuel Ruiz Galán},
journal = {Studia Mathematica},
keywords = {reflexivity; superreflexivity; lack of roughness; convex transitive; second Baire category},
language = {eng},
number = {2},
pages = {175-183},
title = {Dual spaces generated by the interior of the set of norm attaining functionals},
url = {http://eudml.org/doc/284476},
volume = {149},
year = {2002},
}

TY - JOUR
AU - Maria D. Acosta
AU - Julio Becerra Guerrero
AU - Manuel Ruiz Galán
TI - Dual spaces generated by the interior of the set of norm attaining functionals
JO - Studia Mathematica
PY - 2002
VL - 149
IS - 2
SP - 175
EP - 183
AB - We characterize some isomorphic properties of Banach spaces in terms of the set of norm attaining functionals. The main result states that a Banach space is reflexive as soon as it does not contain ℓ₁ and the dual unit ball is the w*-closure of the convex hull of elements contained in the "uniform" interior of the set of norm attaining functionals. By assuming a very weak isometric condition (lack of roughness) instead of not containing ℓ₁, we also obtain a similar result. As a consequence of the first result, a convex-transitive Banach space not containing ℓ₁ and such that the set of norm attaining functionals has nonempty interior is in fact superreflexive.
LA - eng
KW - reflexivity; superreflexivity; lack of roughness; convex transitive; second Baire category
UR - http://eudml.org/doc/284476
ER -