1. The problem statement, all variables and given/known data Is it true/possible to show that in a Hilbert space, if z_n is a sequence (not known to converge a priori) such that (z_n,y)-->0 for all y, then z_n-->0 ? 3. The attempt at a solution I've shown that if z_n converges, then it must be to 0. But does it converge?