Extra problem

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

Note. The hint below contains some greek letters. It may be unreadable in old versions of Netscape (version 4.x, as found on some Unix machines). Newer versions of Netscape/Mozilla, as well as Internet Explorer and Opera, display these characters well. Drop me a hint if you are unable to find a browser that works on this page. Then I'll try to use ps/pdf for this sort of thing in the future.

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.