An An embedding theorem and spectral equality for semigroups involving demicompactness classes
Abstract
Let $(S(t))_{t\geq0}$ and $(T(t))_{t\geq0}$ denote the strongly continuous semigroups of operators in a Banach space $X$. In this paper, we give a sufficient condition guaranteeing that $(S(t))_{t\geq0}$ can be embedded in a $C_{0}$-group on $X$. Moreover, we characterize the demicompactness of $I-(S(t)-T(t))$ for $t>0$. Our theoretical results will be illustrated by investigating the spectral equality for uniformly continuous semigroups for an upper semi-Fredholm spectrum.
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References
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