Exercise 13, § 7

In the Hilbert space $l^2(\mathbf{N})$, let A be the set of points $x = (\xi_n)$ such that we have $\sum_n 2^{2n} \xi_n^2 \leq 1$. Show that A is convex, compact and that it is the closure of the set of its extremal points. \*