Wikipedia:Reference desk/Archives/Mathematics/2017 April 21

= April 21 =

Projections in Hilbert spaces
For each closed subspace K of a Hilbert space H, let $$P_K$$ be the self-adjoint projection onto K. Suppose I have a sequence $$H_0\subset H_1\subset \dots \subset H$$ of closed subsets of H, and let K be the closure of the union of these subspaces. In what operator topology (if any) does the sequence of projection operators $$P_{H_n}$$ tend to the projection operator $$P_K$$? 66.66.228.95 (talk) 00:01, 21 April 2017 (UTC)