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Hamid Boua

Publications and source records attributed to Hamid Boua.

7 recordsLinked to original sources
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↗
arXiv2018

Problem of Descent Spectrum Equality

Let $\mathcal{B}(X)$ be the algebra of all bounded operators acting on an infinite dimensional complex Banach space $X$. We say that an operator $T \in \mathcal{B}(X)$ satisfies the problem of descent spectrum equality, if the descent spectrum of $T$ as an operator coincides with the descent spectrum of $T$ as an element of the algebra of all bounded linear operators on $X$. In this paper we are interested in the problem of descent spectrum equality . Specifically, the problem is to consider the following question: Let $T \in \mathcal{B}(X)$ such that $σ(T)$ has non empty interior, under which condition on $T$ does $σ_{desc}(T)=σ_{desc}(T, \mathcal{B}(X))$ ?

math.SP↗
arXiv2018

Essential Descent Spectrum Equality

A bounded operator $T$ in a Banach space $X$ is said to satisfy the essential descent spectrum equality, if the descent spectrum of $T$ as an operator on $X$ coincides with the essential descent spectrum of $T$. In this note, we give some conditions under which the equality $σ_{desc}(T) = σ^e_{desc}(T)$ holds for a single operator $T$.

math.SP↗