The Dual space of L infty space is not L1 ,are there some example to show this? I am going to use rieze representation thm,but it can not be used because p= $\infty$.

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    $\begingroup$ If the dual of a Banach space is separable, then the original space must be separable. $\endgroup$ – Prahlad Vaidyanathan Jan 14 '15 at 10:58

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