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

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

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)