Hi there. I have this exercise, and I have no idea on how to work it.

It says: LetYbe a closed subspace from a Hilbert spaceH, andPthe orthogonal projection ofHoverY. Demonstrate that:

a) $\displaystyle P^2=PoP=P$ which means, P is an idempotent operator.

b) $\displaystyle P |_Y=Id$ 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.