Let $X$ and $Y$ be two Banach spaces and let $T$ be a linear map between $X$ and $Y$. Show that $T$ is continuous strong-strong if and only if $T$ is continuous weak-weak.
- I can see that $T$ being continuous strong-strong implies that $T$ is continuous strong-weak. How to see weak-weak, please?
- I have no idea on the other direction. Could anyone help me, please? Thank you!