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Essential point spectra of operator matrices trough local spectral theory. (English) Zbl 1148.47004
Given two complex Banach spaces \(X\) and \(Y\), the authors consider the operators on the product space \(X \times Y\) defined by a \(2\times 2\) upper triangular matrix \(M= \left( \begin{matrix} A & C \\ 0 & B \\ \end{matrix} \right)\) and study the set \(\big(\Sigma(A)\cup \Sigma(B)\big)\setminus \Sigma(M)\), where \(\Sigma\) stands for the Browder spectrum, the essential approximate point spectrum, or the Browder essential approximate point spectrum. As an application, they obtain several conditions implying that Browder’s theorem, a-Browder’s theorem, or Weyl’s theorem holds for \(M\).

MSC:
47A10 Spectrum, resolvent
47A11 Local spectral properties of linear operators
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