The imaginary part of the Cesàro operator in \(l^ p\) spaces (Q811661)
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scientific article; zbMATH DE number 4216411
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The imaginary part of the Cesàro operator in \(l^ p\) spaces |
scientific article; zbMATH DE number 4216411 |
Statements
The imaginary part of the Cesàro operator in \(l^ p\) spaces (English)
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1992
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We prove that the matrix kernel determining the imaginary part of the Cesàro operator in \(\ell^ 2\) determines such bounded operators in \(\ell^ p\) \((1<\rho<\infty)\) that the spectra for \(\rho\neq 2\) are not contained in \(R\). This implies that these operators have bad spectral decomposition properties, though the operator in \(\ell^ 2\) is selfadjoint.
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matrix kernel determining the imaginary part of the Cesàro operator
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bad spectral decomposition
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