Continuity of the spectrum on closed similarity orbits (Q1329567)
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scientific article; zbMATH DE number 604805
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Continuity of the spectrum on closed similarity orbits |
scientific article; zbMATH DE number 604805 |
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Continuity of the spectrum on closed similarity orbits (English)
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18 August 1994
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Let \(H\) be a complex Hilbert space, \(T: H\to H\) a continuous linear operator, \(D_ j: H\to H\) an invertible linear operator and suppose that for a continuous linear operator \(T_ 0: H\to H\) we have \[ T_ 0= \lim_{j\to\infty} D_ j TD^{-1}_ j. \] It is shown that if the set \(\{D_ j,D^{-1}_ j: j= 1,2,\dots\}\) is contained in a finite- dimensional subspace, then \(T_ 0\) and \(T\) have equal spectral radii. The method of proof is of separate interest.
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invertible linear operator
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equal spectral radius
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