Let $(T(t))_{t\geq 0}$ be a $C_0$ semigroup of bounded linear operators on a Banach space $X$ and denote its generator by $A$. A fundamental problem to decide whether the Drazin spectrum of each operator $T(t)$ can be obtained from the Drazin spectrum of $A$. In particular, one hopes that the Drazin Spectral Mapping Theorem holds, i.e., $e^{t \sigma_{D}(A)}=\sigma_{D}(T(t))\backslash \{0\}$ for all $t \geq 0$.
@article{38404,
title = {Spectral Mapping Theorem for C0-Semigroups of Drazin spectrum},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {38},
year = {2019},
doi = {10.5269/bspm.v38i3.38404},
language = {EN},
url = {http://dml.mathdoc.fr/item/38404}
}
Tajmouati, Abdelaziz; Boua, Hamid. Spectral Mapping Theorem for C0-Semigroups of Drazin spectrum. Boletim da Sociedade Paranaense de Matemática, Tome 38 (2019) . doi : 10.5269/bspm.v38i3.38404. http://gdmltest.u-ga.fr/item/38404/