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If H_{1}and H_{2}are two Hilbert spaces, prove that one of them is isomorphic to a subspace of the other. (Note that every closed subspace of a Hilbert space is a Hilbert Space.)

What I'm thinking is that every separable Hilbert space is isomorphic to L^{2}. If I recall, a Hilbert space is separable iff it has a countable basis, so what of uncountable bases? Do I then consider a subspace of that space spanned by a countable subset of the uncountable basis?

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# Homework Help: Hilbert Space Isomorphisms

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