Abstract
We study the robustness properties of strong stability of a strongly continuous semigroup on a Hilbert space. We concentrate on a situation where the generator of the unperturbed semigroup has a finite spectral point on the imaginary axis and the resolvent operator is polynomially bounded elsewhere on the imaginary axis. As our main result we present conditions for preservation of the strong stability of the semigroup under bounded perturbations.
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Acknowledgments
The author is grateful to Yuri Tomilov for suggesting the extension of Theorem 2 from finite rank perturbations to perturbations where \(B\) and \(C\) are Hilbert–Schmidt operators.
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Paunonen, L. (2015). On Robustness of Strongly Stable Semigroups with Spectrum on \(i\mathbb {R}\) . In: Banasiak, J., Bobrowski, A., Lachowicz, M. (eds) Semigroups of Operators -Theory and Applications. Springer Proceedings in Mathematics & Statistics, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-319-12145-1_7
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DOI: https://doi.org/10.1007/978-3-319-12145-1_7
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