Exercise 12, § 3

a) Let F be a Hausdorff (DF) space, and $F'_b$ its strong dual. Show that if $F'_b$ is reflexive, then the completion $\hat{F}$ of F is reflexive and is equal to the bidual $F''$ of F (cf. IV, p. 52, exerc. 4 and p. 53, exerc. 11). b) Let E be a Fréchet space. Show that if the bidual $E''$ of E is reflexive, then E is reflexive.