For any natural number n, V(n) denotes a closed linear subspace of a L2(m) Space, which is an Hilbert Space, where m denotes a finite mesure. Moreover (V(n)) is increasing, that is V(n) is a subspace of V(n+1) for any n. Denote by p(n) the orthogonal projection on V(n) and by PV the projection on the closure V of the union of all the V(n). Is it true that p(n) converges to PV in the usual operator norm ? Or does it converges just for some weaker notion of convergence ? Which conditions are required to ensure this ?