Let C and D be two closed convex subsets of a Banach space with C+D is closed. If bounded sequence $\{x_n\}\subset C+D$, can we choose bounded sequences $\{c_n\}\subset C$ and $\{d_n\}\subset D$ such that $x_n=c_n+d_n$ for every n.
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I like the question! Did you already find some answer or a counterexample to it? – dmw64 May 05 '14 at 18:08