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On norm continuity, differentiability and compactness of perturbed semigroups

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Abstract

The main purpose of this paper is to treat semigroup properties like norm continuity, compactness and differentiability for perturbed semigroups in Banach spaces. In particular, we investigate three large classes of perturbations: Miyadera–Voigt, Desch–Schappacher and Staffans–Weiss perturbations. Our approach is mainly based on feedback theory of Salamon–Weiss systems. Our results are applied to abstract boundary integro-differential equations in Banach spaces.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Ibn Zohr University, Hay Dakhla, BP 8106, 80000, Agadir, Morocco

    A. Boulouz, H. Bounit, A. Driouich & S. Hadd

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  1. A. Boulouz
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  2. H. Bounit
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  3. A. Driouich
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  4. S. Hadd
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Correspondence to S. Hadd.

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Communicated by Abdelaziz Rhandi.

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Boulouz, A., Bounit, H., Driouich, A. et al. On norm continuity, differentiability and compactness of perturbed semigroups. Semigroup Forum 101, 547–570 (2020). https://doi.org/10.1007/s00233-020-10138-x

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  • DOI: https://doi.org/10.1007/s00233-020-10138-x

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