= Solution
For a <bounded linear operator> $T$ on a complex <Hilbert space>, the <spectrum of a bounded operator> consists of $\lambda\in\mathbb C$ for which $T-\lambda I$ does not have a bounded everywhere-defined inverse. A bijective bounded operator has a bounded inverse by the <bounded inverse theorem>. Using the disjoint spectral convention,
$$
\boxed{\begin{aligned}
\sigma_p(T)&=\{\lambda:T-\lambda I\text{ is not injective}\},\\
\sigma_c(T)&=\{\lambda:T-\lambda I\text{ is injective, has dense range, but is not onto}\},\\
\sigma_r(T)&=\{\lambda:T-\lambda I\text{ is injective and has nondense range}\}.
\end{aligned}}
$$
These are respectively the <point spectrum>, <continuous spectrum> and <residual spectrum>, and partition the <spectrum>. Some texts let <residual spectrum> include noninjective operators with nondense range; the displayed convention excludes overlap with <point spectrum>.
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