Let $X$ be a Banach space and let $T:X \rightarrow X$ be a bounded linear map.Show that the range of $I - T$ contains the subspace $Y_T = \{x \in X: \limsup_{n\rightarrow \infty} n^2\|T^nx\| < \infty \}$
I have really no good idea how to solve this, any hints would be nice!