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I am reading a book about functional analysis and there is one thing I really don't understand. Let $\mathcal{H}$ be a Hilbert space. And $U \subset \mathcal{H}$ a closed subspace. Is it possible to choose an orthonormal basis $\{e_{i}\}_{i=1}^{\infty}$ such that there exists a subsequence of the $e_{i}$'s that span $U$ ?

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    You've been watching too much Colbert Report :-)2011-10-25
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    my question is: if there exists $B = \{e_{i_{k}}\}_{k=1}^{\infty}$ such that $B$ is an orthonormal basis of $U$?2011-10-25

2 Answers 2