There is a canonical way to associate an element of a Banach space X with its second dual (‘double dual’) space X^{**}. If this mapping is onto, then X is said to be reflexive. We show that Hilbert spaces, l^p and L^p for 1<p<infty, are reflexive. We then prove some general properties of reflexivity, in particular that X is reflexive if and only if X^* is reflexive, and that reflexivity is inherited by subspaces.
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