For each closed subspace K of a Hilbert space H, let ${\displaystyle P_{K}}$ be the self-adjoint projection onto K. Suppose I have a sequence ${\displaystyle H_{0}\subset H_{1}\subset \dots \subset H}$ 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 ${\displaystyle P_{H_{n}}}$ tend to the projection operator ${\displaystyle P_{K}}$? 66.66.228.95 ( talk) 00:01, 21 April 2017 (UTC) reply