Local dual spaces of a Banach space
Volume 147 / 2001
Studia Mathematica 147 (2001), 155-168
MSC: Primary 46B10, 46B20; Secondary 46B04, 46B08.
DOI: 10.4064/sm147-2-4
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 $\ell _1$ admits a smallest local dual.
