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Let $X$ be a reflexive space then show that $X$ is Banach Space and is reflexive in any equivalent norm.

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I am trying it in a following way...

Since dual $X^{'}$ of any normed space $X$ is complete and therefore Banach Space. So, $X^{''}$(double dual) is also Banach space. Now, as $X$ is reflexive we have that $X$ is Banach Space.

But, i am not able to find out any easy way to argue that ..If $X$ is reflexive then it is reflexive in any equivalent norm...

mathonlymath
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    Hints: 1) $X$ is reflexive iff its closed unit ball is weakly compact. 2) A linear operator $T$ between normed spaces is norm-norm continuous iff it is weak-weak continuous. – David Mitra Nov 22 '13 at 09:17
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    The dual only depends on the topology so that an equivalent norm gives the same dual again with an equivalent norm. – Jochen Nov 22 '13 at 11:11

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