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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)[reply]