Hi again Stackexchange,
This is a question I had on an exam today that I could not answer, and it deeply disturbs me.
Let $X$ be a Banach space and $T:X\to X$ a surjective linear map. Show that the adjoint $T^*:X^*\to X^*$ is bounded from below, i.e. there is a $c$ such that $c\Vert g\Vert\leq\Vert T^*\Vert\Vert l\Vert$.
It feels like it should be easy but my mind is frozen.
Thanks in advance.