1. The problem statement, all variables and given/known data Hello, H is a Hilbert space. K is a nonempty, convex, closed subset of H. Prove that the orthogonal projection Pk: H → H, is non-expansive: ll Pk(x) - Pk(y) ll ≤ ll x - y ll 3. The attempt at a solution So the length between the Pk's, which is in K (convex) is less than the distance of x and y, (x and y not in K, I assume.) That's my thought, but I'm getting a bit confused proving it, as I'm mixing things with " ll x - Pk(x) ll ≤ ll x - y ll, " using lenght of vectors. Any hint? Thanks.