Hi there. I have this exercise, and I have no idea on how to work it.
It says: Let Y be a closed subspace from a Hilbert space H, and P the orthogonal projection of H over Y. Demonstrate that:
a) which means, P is an idempotent operator.
b) which means that the P operator restricted to the subspace Y coincides with the identity.
I haven't boarded the problem yet, but when I try it, I'll let you know. I how to read more theory right now, but I'm far from proving this, and perhaps you could help me. I don't even know what the o in PoP means.
Bye there, and thanks in advance.