could anyone help me with this problem. ¡Thankyou very much!
Let H be a Hilbert space.
(a) Let M be a closed subspace of H and let P be a orthogonal projection on M. Prove that P² = P and P is an self-adjoint operator.
(b) Let R ∈ L(H,H) and R²= R and R is self-adjoint. Prove M = Im(R) is a closed subspace of H. Prove that R is the orthogonal projection on M.