In this talk, we study several spectral properties of operator matrices $\begin{pmatrix} A & C \cr Z & B\end{pmatrix}$ acting on an infinite dimensional separable Hilbert space, where the range of $C$ is closed. In particular, we investigate the conditions for such operator matrices to satisfy Weyl's theorem and Weyl type theorems such as $a$-Weyl's theorem, $a$-Browder's theorem, and so on.
This talk is based on joint work with Eungil Ko and Ji Eun Lee.

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