Re: convergence in norm topology

All clear, thanks a lot!

Uzytkownik "arup" <arupkpal@xxxxxxxxx> napisal w wiadomosci
news:1173155593.807622.273560@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Look at the adjoints.

On Mar 5, 7:55 pm, "marcins" <mat...@xxxxxxxxx> wrote:
I've the following problem. If we have a compact, linear map K: H\to H,
where H is Hilbert space, and a sequence of projections onto the finite
dimensional subspaces P_n: H\to H (P_n -> Id strongly) shall we expect
that
KP_n-K ->0? KP_n-K ->0 means convergence in norm topology of bounded
linear
operators. What we know, and this is easy to prove, that P_nK-K ->0.
Improtant thing: P_n doesnt project onto K-invariant subspaces, in
particular onto eigenspaces of K.








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