The imaginary part of the Ces�ro operator inl p spaces
Copyright policy )The imaginary part of the Ces�ro operator inl p spaces
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.
- Eötvös Loránd University Hungary
- Technical University of Berlin Germany
matrix kernel determining the imaginary part of the Cesàro operator, Hermitian and normal operators (spectral measures, functional calculus, etc.), Spectral operators, decomposable operators, well-bounded operators, etc., Spectrum, resolvent, Sobolev (and similar kinds of) spaces of functions of discrete variables, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), bad spectral decomposition
matrix kernel determining the imaginary part of the Cesàro operator, Hermitian and normal operators (spectral measures, functional calculus, etc.), Spectral operators, decomposable operators, well-bounded operators, etc., Spectrum, resolvent, Sobolev (and similar kinds of) spaces of functions of discrete variables, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), bad spectral decomposition
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