Almost invertible operators

We prove that a bounded linear operator $T$ is a direct sum of an invertible operator and an operator with at most countable spectrum iff $0{\text{notinacc}}^{{\omega }_1}\sigma (T),$ where ${\omega }_1$ is the smallest uncountable ordinal and $ac{c}^{{\omega }_1}\sigma (T)$ is the ${\omega }_1$-th Cantor-Bendixson derivative of $\sigma (T)\mathrm{.}$