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Continuous spectrum, point spectrum and residual spectrum of operator matrices. (English) Zbl 1197.47013
Let ${M}_{C}$ denote a $2×2$ upper triangular operator matrix of the form ${M}_{C}=\left(\begin{array}{cc}A& C\\ 0& B\end{array}\right)$, 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 ${\bigcap }_{C\in B\left(Y,X\right)}{\sigma }_{c}\left({M}_{C}\right)$, ${\bigcap }_{C\in B\left(K,H\right)}{\sigma }_{p}\left({M}_{C}\right)$ and ${\bigcap }_{C\in B\left(K,H\right)}{\sigma }_{r}\left({M}_{C}\right)$, where ${\sigma }_{c}\left(·\right)$, ${\sigma }_{p}\left(·\right)$ and ${\sigma }_{r}\left(·\right)$ denote the continuous spectrum, the point spectrum and the residual spectrum, respectively.
##### MSC:
 47A10 Spectrum and resolvent of linear operators
##### References:
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