the $l^2$-critical defocusing nls initial value problem on $\bbb{r}^d$ is known to be locally well-posed for initial data in $l^2$. hamiltonian conservation and the pseudoconformal transformation show that global well-posedness holds for initial data $u_0$ in sobolev $h^1$ and in the weighted space $(1+|x|) u_0 \in l^2$. for the $d=2$ problem, it is known that global well-posedess also holds for data in $h^s$ and also for data in the weighted space $(1+|x|)^{\sigma} u_0 \in l ^2$ for certain $s$, $\sigma < 1$. the talk will presents a new result: if global well-posedness holds in $h^s$ then global well-posedness and scattering holds in the weighted space with $\sigma = s$.