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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-2-4,
author = {Manuel Gonz\'alez and Antonio Mart\'\i nez-Abej\'on},
title = {Local dual spaces of a Banach space},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {155-168},
zbl = {0992.46007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-2-4}
}
Manuel González; Antonio Martínez-Abejón. Local dual spaces of a Banach space. Studia Mathematica, Tome 147 (2001) pp. 155-168. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-2-4/