Every continuous linear functional on a Hilbert space is inner product with a unique vector.Suggest a slogan
Let \(H\) be a Hilbert space and let \(\Lambda\in \dualof{H}\) be a continuous linear functional on \(H\). Then there exists a unique \(y \in H\) such that \[ \Lambda(x) = \inner{x}{y} \quad\text{for all } x\in H . \]