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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

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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).

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  • $\begingroup$ On topological vector spaces it seems there are only books 50 years ago, you know something more modern? $\endgroup$
    – user288972
    Commented Dec 31, 2015 at 19:01
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    $\begingroup$ 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. $\endgroup$ Commented Jan 1, 2016 at 15:36

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