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Demicompactness Properties for Uniformly Continuous Cosine Families

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Abstract

In this paper, we establish some properties for a uniformly continuous cosine family \((C(t))_{t\in \mathbb {R}}\) which has the property that C(t) is demicompact for some (resp. every) \(t>0\). More precisely, we prove that this property is equivalent to the demicompactness of \(I-A\) where A is the infinitesimal generator of the uniformly continuous cosine family \((C(t))_{t\in \mathbb {R}}\). The obtained result is used to study the spectral inclusion for a uniformly continuous cosine family for an upper semi-Fredholm spectrum. In addition, we give some perturbation results on demicompactness.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Road Soukra km 3.5, B.P. 1171,,  3000, Sfax, Tunisia

    Hedi Benkhaled, Asrar Elleuch & Aref Jeribi

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  1. Hedi Benkhaled
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  2. Asrar Elleuch
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  3. Aref Jeribi
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Correspondence to Asrar Elleuch.

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Benkhaled, H., Elleuch, A. & Jeribi, A. Demicompactness Properties for Uniformly Continuous Cosine Families. Mediterr. J. Math. 19, 157 (2022). https://doi.org/10.1007/s00009-022-02083-6

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  • DOI: https://doi.org/10.1007/s00009-022-02083-6

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