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Generalized Weyl spectrum of upper triangular operator matrices. (English) Zbl 1321.47008

Summary: Let \(M_C=\left(\begin{smallmatrix} A & C\\ 0 & B\end{smallmatrix}\right)\) be a \(2\times 2\) upper triangular operator matrix on Hilbert space \(\mathcal H\oplus\mathcal K\). For given operators \(A\in\mathcal B(\mathcal H)\) and \(B\in\mathcal B(\mathcal K)\), sets \(\bigcap_{C\in\mathcal B(\mathcal K,\mathcal H)}\sigma^g_w(M_C)\) and \(\bigcup_{C\in\mathcal B(\mathcal K,\mathcal H)}\sigma^g_w(M_C)\) are investigated, where \(\sigma^g_w(\cdot)\) denotes the generalized Weyl spectrum.

MSC:

47A10 Spectrum, resolvent
47A55 Perturbation theory of linear operators
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