How to show that a Banach space $X$ is reflexive if and only if its dual $X'$ is reflexive?
A Banach space is reflexive if and only if its dual is reflexive
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functional-analysis
banach-spaces
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2First show that if $X'$ is reflexive then $X''$ is reflexive. Then what can you say about $\hat X$? – 2012-06-01
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2@matt: what's $\hat{X}$? – 2012-06-01
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0@t.b. $\hat X$ is canonical embedding of $X$ in $X''$. Sorry I should mentioned this. – 2012-06-01