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Re: countable set of closed subspaces in separable Hilbert space question
Posted:
Nov 11, 2012 11:24 AM
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On Sat, 10 Nov 2012 20:46:42 -0800 (PST), "Daniel J. Greenhoe"
<dgreenhoe@yahoo.com> wrote:
>Let H be a separable Hilbert space.
>Let (X_n) be a sequence of nested subspaces in H such that
> X_n subset X_{n+1}, X_n not= X_{n+1}.
>What is the relationship between the following two conditions in H?
> 1. closure{ Union X_n } = H
> 2. closure{ lim_{n->infty} X_n } = H
>Does one imply the other? Are they equivalent?
I can't imagine what you mean by lim_{n->infty} X_n
other than the union.
???
>Pointers to good references are especially appreciated.
>Many thanks in advance,
>Dan
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