Let $X$ be a Banach space and $T: X \to X$ be bounded and invertible.
Is it true that the Fredholm index $\mathrm{ind}(T) = 0$?
2026-04-06 17:32:56.1775496776
Fredholm index of invertible bounded operator
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Yes, because both the kernel and the cokernel of $T$ are trivial.