1. The problem statement, all variables and given/known data This is a problem from Haim Brezis's functional analysis book. 2. Relevant equations 3. The attempt at a solution I'm assuming (e)n is the vectors like (e)1 = (1,0,0), (e)2=(0,1,0) and so on. We know every hilbert space has an orthonormal basis. I also need to know the difference between l^2 and L^2 spaces. I know that this might not be much of a solution, but I'm really stuck.