So I have a homework question which I have no idea how to start.
Let $E_0$ be a dense subspace of the normed space $E$. Let $T_0:E_0 \rightarrow F$ be a bounded linear operator into the Banach space $F$.
(i) Show that $T_0$ can be uniquely extended to a bounded linear operator $T:E \rightarrow F$.
(ii) Prove that $\|T\| = \|T_0\|$.
Any hints would be much appreciated!