Geodesic
Relative demicompactness properties for exponentially founded $C$-semigroups
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2022), pp. 3-12

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Let $C$ be an invertible bounded linear operator on a Banach space $X$. In this paper, we use the concept of relative demicompactness in order to investigate some properties for an exponentially bounded $C$-semigroup $(T(t))_{t\geq0}$. More precisely, we prove that the relative demicompactness of $T(t)$ for some positive values of $t$ is equivalent to the relative demicompactness of $C-A$ where $A$ is the infinitesimal generator of $(T(t))_{t\geq0}$. In addition, 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 $AC$.
Keywords: C-semigroup, relative demicompact linear operator, Hilbert space. 
@article{IVM_2022_6_a0,
     author = {H. Benkhaled and A. Elleuch and A. Jeribi},
     title = {Relative demicompactness properties for exponentially founded $C$-semigroups},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--12},
     publisher = {mathdoc},
     number = {6},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_6_a0/}
}
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H. Benkhaled; A. Elleuch; A. Jeribi. Relative demicompactness properties for exponentially founded $C$-semigroups. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2022), pp. 3-12. http://geodesic.mathdoc.fr/item/IVM_2022_6_a0/