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Topic: countable set of closed subspaces in separable Hilbert space question
Replies: 14   Last Post: Nov 13, 2012 10:29 PM

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William Elliot

Posts: 2,637
Registered: 1/8/12
Re: countable set of closed subspaces in separable Hilbert space

Posted: Nov 11, 2012 10:21 PM
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On Sun, 11 Nov 2012, Daniel J. Greenhoe wrote:

> On Sunday, November 11, 2012 5:09:34 PM UTC+8, William Elliot wrote:
> > ...Do you mean the topological closure or some algebra construction?
> > How are you defining lim(n->oo) X_n?

> "Strong convergence" ("convergence in the norm"); that is, the norm
> induced by the inner product:

> For any e>0 there exists N such that
> || x-x_n || < e for all n>N

That's the usual definition for a sequence of points
to converge to a point. It has nothing to do with
a sequence of subsets or subspaces converging to a
set or subspace. How for example, are you defining
||X - X_n|| for sets X and X_n?

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