
Re: countable set of closed subspaces in separable Hilbert space question
Posted:
Nov 11, 2012 10:21 PM


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 >  xx_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?

