For every continuous linear functional $f$ on a Hilbert space $\mathcal{H}$ , there is a unique $u\in \mathcal{H}$ such that $f(x)=\langle x,u \rangle$ for all $x\in\mathcal{H}$ .
Note: $\langle x,u \rangle$ denotes the inner product between $x$ and $u$ .