arXiv subjects
Publications and source records attributed to M. Amouch.
Let $(T(t))_{t\geq0}$ be a $C_0$ semigroups and $A$ be its infinitesimal generator. In this work, we prove that the spectral inclusion for $(T(t))_{t\geq0}$ remains true for the Drazin invertible and Quasi-Fredholm spectra. Also, we will give conditions under which facts $A$ is quasi-Fredholm, $A$ is Drazin invertible and $A$ is B-Fredholm are equivalent.
In this paper, we give conditions for which the $C_0$ semigroups satisfies spectral equality for semiregular, essentially semiregular and semi-Fredholm spectrum. Also, we establish the spectral inclusion for B-Fredholm spectrum of a $C_0$ semigroups.
Let $X$ a Banach space and $T$ a bounded linear operator on $X.$ We denote by $S(T)$ the set of all $λ\in \cit$ such that $T$ does not have the single-valued extension property at $λ$. In this note we prove equality up to $S(T)$ between the left Drazin spectrum and the left B-Fredholm spectrum and between the semi-essential approximate point spectrum and the left Drazin spectrum. As applications we investigate generalized Weyl's theorem for operator matrices and multipliers operators.