I am trying to gather all I can know about the weak topology on a separable (infinite dimensional) Hilbert space. As far as I know, this space is :
- Hausdorff Locally convex
- compact on weakly-closed bounded subsets
- metrizable on bounded subsets
(And it is not : complete, first-countable, metrizable, quasibarrelled)
I want to know weather or not this topological vector space is :
I'm sure this is common knowledge but it's hard to find references on those specific questions.