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Feb 22, 2020 at 9:13 comment added Tomasz Kania @WlodAA, yes, the ball is not weak*-separable as $JL_2$ does not embed into $\ell_\infty$.
Feb 22, 2020 at 5:04 comment added Wlod AA I trust you. :)
Feb 22, 2020 at 1:30 comment added Wlod AA Tomek, is the said unit ball not separable under the topology induced by the weak* topology of $X^*$?
Feb 21, 2020 at 21:41 history answered Tomasz Kania CC BY-SA 4.0