Incomplete-domain counterexample to closed-graph factorization
= Incomplete-domain counterexample to closed-graph factorization
On incomplete $c_{00}$ with the $\ell^2$ norm, let $S(x_n)=(x_n/n)$ and let $T$ be inclusion into $\ell^2$. Their images agree, but $S^{-1}T(e_n)=ne_n$ is unbounded.