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Spectra of upper-triangular operator matrices. (Chinese. English summary) Zbl 1235.47010
Summary: Let $X$ and $Y$ be Banach spaces, $A\in B (X)$, $B\in B (Y)$, $C\in B (Y, X)$, $M_C=\pmatrix A&C\\0&B\endpmatrix$ 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.

47A10Spectrum and resolvent of linear operators
47A62Equations involving linear operators, with operator unknowns
Full Text: arXiv