Local dual spaces of a Banach space

Manuel González ¹   ; Antonio Martínez-Abejón ²

¹ Departamento de Matemáticas Facultad de Ciencias Universidad de Cantabria E-39071 Santander, Spain
² Departamento de Matemáticas Facultad de Ciencias Universidad de Oviedo E-33007 Oviedo, Spain

Studia Mathematica, Tome 147 (2001) no. 2, pp. 155-168

Résumé

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 $\ell _1$ admits a smallest local dual.

Détail

DOI : 10.4064/sm147-2-4

Keywords: study local dual spaces banach space which described subspaces * have properties principle local reflexivity attributes subspace ** several characterizations local dual spaces which allow many examples moreover every separable space has separable local dual choose metric approximation property has separable space containing copies ell admits smallest local dual