## Description of extended eigenvalues and extended eigenvectors of integration operators on the Wiener algebra.(English)Zbl 1172.47002

The author gives a characterization of the extended eigenvalues and eigenvectors of the integral operator $$Vf(z)= \int_0^z f(t)\,dt$$ in the Wiener algebra $$\{f(z)=\sum_{n=0}^\infty a_nz^n: \sum_{n=0}^\infty |a_n| <\infty\}$$, that is, those complex numbers $$\lambda$$ and bounded operators $$A$$ on the Wiener algebra such that $$VA=\lambda AV$$. A similar result for some weighted shift operators on $$\ell_p$$ spaces is given as well.

### MSC:

 47A10 Spectrum, resolvent 47B38 Linear operators on function spaces (general) 46J15 Banach algebras of differentiable or analytic functions, $$H^p$$-spaces
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### References:

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