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Let $E$ be a normed vector space and suppose that two norms $\| \, \|_1$ and $\| \, \|_2$ are equivalent. We are asked that if $E$ is reflexive with respect to $\| \, \|_1$, is $E$ also reflexive with respect to $\| \, \|_2$?

What does it mean to be reflexive with respect to a norm? How is it related to the canonical bijection $x \mapsto Jx$?

Andy Tam
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    When we talk about bounded linear functionals, then there must be an underlying norm. Thus when you talk about the dual space, it is in fact the dual space with respect to a norm. – Frank Lu Nov 13 '16 at 04:41
  • So this really has nothing to do with $Jx$ except that it has norm $|Jx|{E^{**}} = |x|{E}$? – Andy Tam Nov 14 '16 at 18:41

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