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Timeline for A particular separation example

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May 12, 2018 at 9:09 comment added Tomasz Kania @AliBagheri, certainly $\ell_1^*$ is not norm-separable, however, it is weak*-separable (as is $\ell_1^{**}$). You may be interested in this paper: carma.newcastle.edu.au/brailey/Research_papers/…
May 11, 2018 at 19:40 comment added ABB $\ell_1$ is separable then its second dual $X=\ell_\infty^{*}$ is weak star separable. But its dual is not separable any more. Right?
May 11, 2018 at 14:48 comment added ABB Thanks. Any example of separable locally convex space $X$ whose dual is not weak*-separable? Perhaps it serves an answer for Q2!
May 11, 2018 at 14:46 vote accept ABB
May 11, 2018 at 14:39 history answered Tomasz Kania CC BY-SA 4.0