
countable set of closed subspaces in separable Hilbert space question
Posted:
Nov 10, 2012 11:46 PM


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? Pointers to good references are especially appreciated. Many thanks in advance, Dan

