Remark

— If E is a Hausdorff prehilbertian space and $\hat{E}$ the hilbertian space completion of E, we know (III, p. 16) that the dual E' of E can be identified with the dual of $\hat{E}$; it then follows from th. 3 (V, p. 15) that every continuous linear form on E can be written in a unique way as $x \mapsto \langle a|x \rangle$, where $a \in \hat{E}$.