Let $Y$ be a subspace of a Banach space $X$.
How can I show that there exists an 1-1 isometric map $\phi\colon Y^*\to X^*$ (need not be linear)?
Also, how can I show that $X^*|_{Y}=Y^*$? Here, $X^*|_{Y}$ is the set of restriction to $Y$ of all $f\in X^*$.