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ON SUBSPACE-SUPERCYCLIC SEMIGROUP
El Berrag, Mohammed,Tajmouati, Abdelaziz Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.1
A $C_0$-semigroup ${\tau}=(T_t)_{t{\geq}0}$ on a Banach space X is called subspace-supercyclic for a subspace M, if $\mathbb{C}Orb({\tau},x){\bigcap}M=\{{\lambda}T_tx\;:\;{\lambda}{\in}\mathbb{C},\;t{\geq}0\}{\bigcap}M$ is dense in M for a vector $x{\in}M$. In this paper we characterize the notion of subspace-supercyclic $C_0$-semigroup. At the same time, we also provide a subspace-supercyclicity criterion $C_0$-semigroup and offer two equivalent conditions of this criterion.
SPECTRA ORIGINATED FROM FREDHOLM THEORY AND BROWDER'S THEOREM
Amouch, Mohamed,Karmouni, Mohammed,Tajmouati, Abdelaziz Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.3
We give a new characterization of Browder's theorem through equality between the pseudo B-Weyl spectrum and the generalized Drazin spectrum. Also, we will give conditions under which pseudo B-Fredholm and pseudo B-Weyl spectrum introduced in [9] and [25] become stable under commuting Riesz perturbations.
CESÀRO-HYPERCYCLIC AND HYPERCYCLIC OPERATORS
El Berrag, Mohammed,Tajmouati, Abdelaziz Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.2
In this paper we provide a $Ces{\grave{a}}ro$-hypercyclicity criterion and offer two examples of this criterion. At the same time, we also characterize other properties of $Ces{\grave{a}}ro$-hypercyclic operators.
The Drazin inverse of the sum of two products
Safae Alaoui Chrifi,Abdelaziz Tajmouati 대한수학회 2022 대한수학회논문집 Vol.37 No.3
In this paper, for bounded linear operators $A,B,C$ satisfying $[AB,B]=[BC,B]=[AB,BC]=0$ we study the Drazin invertibility of the sum of products formed by the three operators $A,B$ and $C$. In particular, we give an explicit representation of the anti-commutator $\{A,B\}=AB+BA$. Also we give some conditions for which the sum $A+C$ is Drazin invertible.