Characterization of subspace
Posted: Wed Nov 11, 2015 3:51 pm
Let \(\displaystyle{\left(X,||\cdot||\right)}\) be an \(\displaystyle{\mathbb{R}}\) - normed space and \(\displaystyle{Y}\)
be \(\displaystyle{\mathbb{R}}\) - linear subspace of \(\displaystyle{X}\) . Show that
$$\overline{Y}=\cap\,\left\{\rm{Ker}(f): f\in X^{\star}\,,Y\subseteq \rm{Ker}(f)\right\}$$
be \(\displaystyle{\mathbb{R}}\) - linear subspace of \(\displaystyle{X}\) . Show that
$$\overline{Y}=\cap\,\left\{\rm{Ker}(f): f\in X^{\star}\,,Y\subseteq \rm{Ker}(f)\right\}$$