
Re: countable set of closed subspaces in separable Hilbert space question
Posted:
Nov 11, 2012 11:24 AM


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

