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Weyl spectra of operator matrices. (English) Zbl 0965.47011
The author studies Fredholm properties of the operator matrix $M_C = \left(\smallmatrix A & C \\ 0 & B\endsmallmatrix \right)$ for operators in Hilbert spaces. Let $\omega (T)$ denote the Weyl spectrum of an operator $T$, i.e., the set of all complex $\lambda$ such that $\lambda -T$ is not a Fredholm operator of index zero. The main result of the paper reads as follows: $\omega (A) \cup \omega (B) = \omega (M_C) \cup \kappa$, where $\kappa$ is the union of some holes in $\omega (M_C)$ which are contained in $\omega (A) \cap \omega (B)$. This implies that the Weyl spectral radius of $M_C$ is independent of $C$.

47A53(Semi-) Fredholm operators; index theories
47A55Perturbation theory of linear operators
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