Dual topology and Mackey–Arens theorem

Question

I read only by wikipedia the Mackey–Arens theorem, that is:

Given dual pair $(X, X')$ with $X$ a locally convex space and $X'$ its continuous dual, then $\mathcal{T}$ is a dual topology on $X$ if and only if it is a topology of uniform convergence on a family of absolutely convex and weakly compact subsets of $X'$.

You know recommend good books in which to study these topics?

thank you

Answer 1

Chapter IV of H.H. Schaefer, Topological Vector Spaces (GTM 3). When you are done you could improve the wikipedia article...

A more recent reference would be chapter 23 in Meise and Vogt, Introduction to Functional Analysis (Clarendon).