On a theorem of Carey and Pincus (Q915093)
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scientific article; zbMATH DE number 4151157
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a theorem of Carey and Pincus |
scientific article; zbMATH DE number 4151157 |
Statements
On a theorem of Carey and Pincus (English)
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1990
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A new proof is given of the following theorem due to \textit{R. W. Carey} and \textit{J. D. Pincus} [Am. J. Math. 98, 481-514 (1976; Zbl 0362.47007)]: If H is a bounded selfadjoint operator with spectral measure singular with respect to Lebesgue measure, then there exists a selfadjoint V of arbitrarily small trace-norm such that \(H+V\) has pure point spectrum. This result is extended as follows: If, moreover, H has finite spectral multiplicity r, then V can be chosen of rank r.
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singular continuous spectrum
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perturbation of spectrum
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bounded selfadjoint operator with spectral measure singular with respect to Lebesgue measure
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arbitrarily small trace-norm
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pure point spectrum
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finite spectral multiplicity
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