I have a Banach Space $X$ and an linear continuous operator $T\colon X\to X$ that has finite rank (i.e. $\dim {T(X)}<\infty$). Then,
$I-T$ is injective if and only if $I-T$ is surjective?
I have a Banach Space $X$ and an linear continuous operator $T\colon X\to X$ that has finite rank (i.e. $\dim {T(X)}<\infty$). Then,
$I-T$ is injective if and only if $I-T$ is surjective?