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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?

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    Look up the [Fredholm alternative](http://en.wikipedia.org/wiki/Fredholm_alternative) see also [here](http://www.math.ksu.edu/~ramm/papers/419amm.pdf).2012-01-06

2 Answers 2