Local dual spaces of a Banach space

Manuel González, and Antonio Martínez-Abejón. "Local dual spaces of a Banach space." Studia Mathematica 147.2 (2001): 155-168. <http://eudml.org/doc/285152>.

@article{ManuelGonzález2001,
abstract = { We study the local dual spaces of a Banach space X, which can be described as the subspaces of X* that have the properties that the principle of local reflexivity attributes to X as a subspace of X**. We give several characterizations of local dual spaces, which allow us to show many examples. Moreover, every separable space X has a separable local dual Z, and we can choose Z with the metric approximation property if X has it. We also show that a separable space containing no copies of ℓ₁ admits a smallest local dual. },
author = {Manuel González, Antonio Martínez-Abejón},
journal = {Studia Mathematica},
keywords = {local dual space; local reflexivity; norming subspace; smallest local dual},
language = {eng},
number = {2},
pages = {155-168},
title = {Local dual spaces of a Banach space},
url = {http://eudml.org/doc/285152},
volume = {147},
year = {2001},
}

TY - JOUR
AU - Manuel González
AU - Antonio Martínez-Abejón
TI - Local dual spaces of a Banach space
JO - Studia Mathematica
PY - 2001
VL - 147
IS - 2
SP - 155
EP - 168
AB - We study the local dual spaces of a Banach space X, which can be described as the subspaces of X* that have the properties that the principle of local reflexivity attributes to X as a subspace of X**. We give several characterizations of local dual spaces, which allow us to show many examples. Moreover, every separable space X has a separable local dual Z, and we can choose Z with the metric approximation property if X has it. We also show that a separable space containing no copies of ℓ₁ admits a smallest local dual.
LA - eng
KW - local dual space; local reflexivity; norming subspace; smallest local dual
UR - http://eudml.org/doc/285152
ER -