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


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).

  • $\begingroup$ On topological vector spaces it seems there are only books 50 years ago, you know something more modern? $\endgroup$ – Andrew Dec 31 '15 at 19:01
  • $\begingroup$ Abstract functional analysis became less fashionable after its peak in the 1960's-70's and I actually leafed through 4-5 books before stumbling on Schaefer. But your comment made me look further and I found Meise and Vogt recommended in an old SE reply. $\endgroup$ – Justpassingby Jan 1 '16 at 15:36

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