Dense subspace
Posted: Sat Jan 16, 2016 12:04 am
Let \(\displaystyle{\left(X,||\cdot||\right)}\) be an \(\displaystyle{\mathbb{R}}\) - normed space and \(\displaystyle{Y}\) a
subspace of \(\displaystyle{\left(X,+,\cdot\right)}\) such that, if \(\displaystyle{f\in X^{\star}=\mathbb{B}(X,\mathbb{R})}\) with \(\displaystyle{f|_{Y}=\mathbb{O}}\) , then
\(\displaystyle{f=\mathbb{O}}\) . Prove that \(\displaystyle{Y}\) is dense on \(\displaystyle{\left(X,||\cdot||\right)}\) .
subspace of \(\displaystyle{\left(X,+,\cdot\right)}\) such that, if \(\displaystyle{f\in X^{\star}=\mathbb{B}(X,\mathbb{R})}\) with \(\displaystyle{f|_{Y}=\mathbb{O}}\) , then
\(\displaystyle{f=\mathbb{O}}\) . Prove that \(\displaystyle{Y}\) is dense on \(\displaystyle{\left(X,||\cdot||\right)}\) .