Why is the following operator invertible – math.stackexchange.com

Why is the following operator invertible – math.stackexchange.com

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Suppose that $T : X \rightarrow X$ is an isometry between two Banach spaces. Then if $|\lambda| < 1$, then $T^{-1} - \frac{1}{\lambda}I_X$ is invertible. Can someone explain this step as it is ...

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