The question comes from the following link on page 25: https://www.ucl.ac.uk/~ucahad0/3103_handout_3.pdf
They prove $(T^{-1})^*=(T^*)^{-1}$, but I don't see how it proves $T^*$ is a topological isomorphism.
2026-03-26 13:51:31.1774533091
If $T$ is a topological isomorphism, then so is $T^*$
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Thanks to Randall, I was able to figure it out.
$T^*$ having an inverse implies it is bijective. We also know the adjoint is bounded and linear. We can use this to show $T^*$ is a topological isomorphism.