Poincare-Dulac normal form reduction for unconditional well-posedness of the periodic cubic NLS

We implement an infinite iteration scheme of Poincare-Dulac normal form reductions to establish an energy estimate on the one-dimensional cubic nonlinear Schrodinger equation (NLS) in CtL2(T), without using any auxiliary function space. This allows us to construct weak solutions of NLS in CtL2(T) with initial data in L2(T) as limits of classical solutions. As a consequence of our construction, we also prove unconditional well-posedness of NLS in Hs(T) for Hs? 1/6.