
Re: countable set of closed subspaces in separable Hilbert space question
Posted:
Nov 11, 2012 12:56 AM


On Sat, 10 Nov 2012, Daniel J. Greenhoe 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}.
Vectorial subspaces or topological subspaces?
> 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?
Is there a difference between lim(n>oo) X_n and \/_n X_n?
Closure in the topological sense?

