I don't see how to solve this problem which I think should be easy:
Let Y be a reflexive space. Assume $Y$ is continuously embedded in a Hilbert space $H$ and $Y$ is dense in $H$. Show that $H^*$ is dense in $Y^*$. I already know that $H^*$ is continuously embedded in $Y^*$ so you may use that if it helps.
Any help would be appreciated, thanks.