Riesz Representation Theorem (Hilbert Spaces)/Corollary

Corollary to Riesz Representation Theorem (Hilbert Spaces)
Let $H$ be a Hilbert space.

Let $L$ be a bounded linear functional on $H$.

Let $h_0 \in H$ be such that:


 * $\forall h \in H: L h = \innerprod h {h_0}$

The norm of $L$ satisfies:


 * $\norm L = \norm {h_0}$

Proof
So:
 * $\norm L \le \norm {h_0}$

Also,:

So $\norm {h_0} \le \norm L$.