I knew that the dual space of $\ell^1$, a separable space is not reflexive because its dual space is $\ell^\infty$, which is not separable. But, I do not know whether $\ell^\infty$ is reflexive or not because I was unable to use the result on the relation between separability and reflexivity to prove it. Is there any hint on this?
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3Does https://math.stackexchange.com/questions/152343/a-banach-space-is-reflexive-if-and-only-if-its-dual-is-reflexive answer your question? – Nate Eldredge Dec 29 '19 at 02:04
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I guess you mean to say that $\ell^1$ is NOT reflexive, and you are asking whether $\ell^\infty$ is? – Nate Eldredge Dec 29 '19 at 02:04
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Yes, I have edited the question. Sorry. – Nothing Dec 29 '19 at 02:27