Let $V \subset H$ where $H$ is Hilbert space. Let $T:H^* \to V^*$ be the canonical map that restricts the domain of a functional in $H$ so that it's a functional in $V$.
How do I show that $\lVert T\varphi \rVert_{V^*} \leq C\lVert \varphi \rVert_{H^*}$ if $\lVert v \rVert_H \leq C\lVert v \rVert_V$? I can't get it out...
Also, how to show that
$Range(T)$ is dense in $V^*$ if $V$ is reflexive?
No idea where to start with this. I only know that reflexive means $V \equiv V^{**}$.