Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
William Elliot

Posts: 1,704
Registered: 1/8/12
Re: countable set of closed subspaces in separable Hilbert space
question

Posted: Nov 11, 2012 10:21 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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?




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.