Let $T$ be a real torus, and let $X$ and $Y$ be $T$-spaces. Under what conditions (if any) will the existence of graded $H^*_T$-algebra isomorphism between the $T$-equivariant cohomologies of $X$ and $Y$ (say over the rationals) imply the existence of a T-equivariant homotopy equivalence between $X$ and $Y$?