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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
##### Keywords:
operator matrices; Browder’s theorem; Weyl’s theorem
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##### References:
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