Exercise 5, § 2

Let $E$ be a Hausdorff locally convex space, and $E'$ its dual. a) In order that the strong topology on $E'$ be identical with $\tau(E', E)$, it is necessary and sufficient that $E$ is semi-reflexive. b) Suppose that $E$ is infra-barrelled. In order that the strong topology on $E'$ be identical with the topology of compact convergence, it is necessary and sufficient that $E$ be a Montel space.