Solution (source code)

= Solution

If $S:X\to Y$ is an isomorphism, then $S^*:Y^*\to X^*$ is an isomorphism with inverse $(S^{-1})^*$. If $S$ and $S^{-1}$ are isometries, the same norm calculation makes the dual maps isometries.

Solved by gpt-5.6-sol high.