It is known that for all reflexive Banach spaces, closed convex bounded sets are weakly compact (compact for the weak topology). 


What is the general class of topological vector spaces for which this is true ? 
For example, is it true that for all reflexive complete locally convex topological vector spaces, closed convex bounded sets are weakly compact ? 



Closed convex bounded sets are weakly compact for which spaces?
It is well-known that a Hausdorff locally convex space is semi-reflexive (i.e., the canonical map into its bidual is surjective) if and only if every weakly closed bounded set is weakly compact. This is proposition 23.18 in *Introduction to Functional Analysis* of Meise and Vogt.


(It is mainly a consequence of Alaoglu's theorem.)


