arXiv subjects

Mohammed Karmouni

Publications and source records attributed to Mohammed Karmouni.

3 recordsLinked to original sources

arXiv2019

Generalized Drazin-Riesz Invertibility for Operators Matrices

Let $A\in\mathcal{B}(X)$, $B\in\mathcal{B}(Y)$ and $C\in\mathcal{B}(Y,X)$ where $X$ and $Y$ are infinite Banach or Hilbert spaces. Let $M_{C}=\begin{pmatrix} A & C\cr 0 & B \end{pmatrix}$ be $2\times 2$ upper triangular operator matrix acting on $X\oplus Y$. In this paper, we consider some necessary and sufficient conditions for $M_{C}$ to be generalized Drazin-Riesz invertible. Furthermore, the set $\bigcap_{C\in \mathcal{B}(Y,X)}σ_{gDR}(M_{C})$ will be investigated and their relation between $\bigcap_{C\in \mathcal{B}(Y,X)}σ_{b}(M_{C})$ will be studied, where $σ_{gDR}(M_{C})$ and $σ_{b}(M_{C})$ denote the generalized Drazin-Riesz spectrum and the Browder spectrum, respectively.

math.FA↗

arXiv2018

Limit Points for Browder Spectrum of Operator Matrices

Let $A\in \mathcal{B}(X)$ and $B\in \mathcal{B}(Y)$, where $X$ and $Y$ are Banach spaces, and let $M_{C}$ be an operator acting on $X\oplus Y$ given by $M_C=\begin{pmatrix} A & C \\ 0 & B \\ \end{pmatrix}$. We investigate the limit point set of the Browder spectrum of $M_{C}$. It is shown that $$ acc σ_{b}(M_C)\cup W_{acc σ_{b}}= acc σ_{b}(A)\cup acc σ_{b}(B)$$ where $W_{acc σ_{b}}$ is a subsets of $ accσ_{*}(B)\cap accσ_{*}(A)$ and a union of certain holes in $ acc σ_{b}(M_C)$. Furthermore, several sufficient conditions for $accσ_{b}(M_C)=accσ_{b}(A)\cup accσ_{b}(B)$ holds for every $C\in \mathcal{B}(Y,X)$ are given.

math.FA↗

arXiv2018

Spectral mapping theorems of differentiable C0 semigroups

Let $(T(t))_{t\geq 0}$ be a $C_0$ semigroup on a Banach space $X$ with infinitesimal generator $A$. In this work, we give conditions for which the spectral mapping theorem $σ_{*}(T(t))\backslash \{0\}=\{e^{λs}, λ\inσ_{*}(A)\}$ holds, where $σ_*$ can be equal to the essential, Browder and Kato spectrum. Also, we will be interested in the relations between the spectrum of $A$ and the spectrum of the nth derivative $T(t)^{(n)}$ of a differentiable $C_0$ semigroup $(T(t))_{t\geq0}$.

math.SP↗