*Prove that a closed subspace of a reflexive space is reflexive.*

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*Hint.* Let *X* be reflexive and *Y* a closed subspace. If η belongs to *Y*^{**}, consider the functional ξ on *X*^{*} defined by ξ(*f*)=η(*f*|_{Y}), where *f*|_{Y} is the restriction of *f* to *Y*. Use the fact that *X* is reflexive to represent ξ by a vector *x* in *X*. Then show that *x* must in fact belong to *Y*. The Hahn–Banach theorem will come in handy for this last part.