\(a\)-Weyl's theorem for operator matrices (Q2759019)
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scientific article; zbMATH DE number 1680679
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(a\)-Weyl's theorem for operator matrices |
scientific article; zbMATH DE number 1680679 |
Statements
10 December 2001
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Weyl spectrum
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essential approximate point spectrum
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Browder essential approximate point spectrum
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\(a\)-Weyl's theorem
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Weyl's theorem
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\(a\)-Browder's theorem
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Browder's theorem
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0.9588738
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0.9548485
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0.95012224
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0.9389913
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0.93162924
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0.9296424
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0.92630875
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\(a\)-Weyl's theorem for operator matrices (English)
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It is shown by the authors that if NEWLINE\[NEWLINEM_c= \begin{pmatrix} A & C\\ 0 & B\end{pmatrix}NEWLINE\]NEWLINE is a \(2\times 2\) upper triangular matrix on the Hilbert space \(H\oplus K\), then \(a\)-Weyl's theorem for \(A\) and \(B\) need not imply \(a\)-Weyl's theorem for \(M_c\) even when \(C= D\). The authors also discuss how \(a\)-Weyl's theorem and \(a\)-Browder's theorem behave for \(2\times 2\) operator matrices on the Hilbert space.
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