Continuous spectrum, point spectrum and residual spectrum of operator matrices (Q977484)

Let \(M_C\) denote a \(2\times 2\) upper triangular operator matrix of the form \(M_C=\left(\begin{smallmatrix} A&C\\0&B\end{smallmatrix}\right)\), which is acting on the sum of Banach spaces \(X\oplus Y\) or Hilbert spaces \(H\oplus K\). The authors of this paper characterize the sets \(\bigcap_{C\in B(Y,X)} \sigma_c(M_C)\), \(\bigcap_{C\in B(K,H)} \sigma_p(M_C)\) and \(\bigcap_{C\in B(K,H)} \sigma_r(M_C)\), where \(\sigma_c(\cdot)\), \(\sigma_p(\cdot)\) and \(\sigma_r(\cdot)\) denote the continuous spectrum, the point spectrum and the residual spectrum, respectively.