Abstract
Let C be an invertible bounded linear operator in Banach space X. In this paper, we use the concept of relative demicompactness in order to study some properties of an exponentially bounded C-semigroup (T(t))t ≥ 0. More precisely, we prove that the relative demicompactness of T(t) at some positive values of t is equivalent to relative demicompactness of C – A where A is the infinitesimal generator of (T(t))t ≥ 0. Besides, we study the relative demicompactness of the resolvent. Finally, we present some conditions on exponentially bounded C-semigroups in Hilbert space guaranteeing the relative demicompactness of AC.
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ACKNOWLEDGMENTS
The authors thank Professor S. Piskarev for valuable comments and advice on this paper.
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Translated by A. Ivanov
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Hedi Benkhaled, Elleuch, A. & Jeribi, A. Relative Demicompactness Properties for Exponentially Bounded C 0-Semigroups. Russ Math. 66, 1–7 (2022). https://doi.org/10.3103/S1066369X22060019
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DOI: https://doi.org/10.3103/S1066369X22060019