Give a simple proof of the Distance Attaining Functional Lemma if X is assumed to be...

 

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Give a simple proof of the Distance Attaining Functional Lemma if X is assumed to be a Hilbert space. (Hint: Consider f(x) = (x-Pw (a), (x-Pw (ro))/x-Pw (ro)||), where W is the closure of Y. Carefully verify that f is the desired functional.) Give a simple proof of the Distance Attaining Functional Lemma if X is assumed to be a Hilbert space. (Hint: Consider f(x) = (x-Pw (a), (x-Pw (ro))/x-Pw (ro)||), where W is the closure of Y. Carefully verify that f is the desired functional.)