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Spectra of upper-triangular operator matrices. (Chinese) Zbl 1235.47010
Summary: Let $X$ and $Y$ be Banach spaces, $A\in B\left(X\right)$, $B\in B\left(Y\right)$, $C\in B\left(Y,X\right)$, ${M}_{C}=\left(\begin{array}{cc}A& C\\ 0& B\end{array}\right)$ be the operator matrix acting on the Banach space $X\oplus Y$. In this paper, we present 20 kinds of spectral structures of ${M}_{C}$, decide 18 kinds of spectral filling-in-hole properties of ${M}_{C}$ and present some interesting examples of these problems.
##### MSC:
 47A10 Spectrum and resolvent of linear operators 47A62 Equations involving linear operators, with operator unknowns
##### Keywords:
Banach spaces; upper-triangular operator matrices; spectra