Zobrazeno 1 - 10
of 143
pro vyhledávání: '"Amouch, P."'
An operator $T$ acting on a separable complex Hilbert space $H$ is said to be hypercyclic if there exists $f\in H$ such that the orbit $\{T^n f:\ n\in \mathbb{N}\}$ is dense in $H$. Godefroy and Shapiro \cite{GoSha} characterized those elements in th
Externí odkaz:
http://arxiv.org/abs/2307.02271
Autor:
Mohamed Amouch, Hamza Lakrimi
Publikováno v:
Mathematica Bohemica, Vol 149, Iss 1, Pp 1-11 (2024)
Let $X$ be a Banach space, $\mathcal{B}(X)$ the algebra of bounded linear operators on $X$ and $(J, \|{\cdot}\|_J)$ an admissible Banach ideal of $\mathcal{B}(X)$. For $T\in\mathcal{B}(X)$, let $L_{J, T}$ and $R_{J, T}\in\mathcal{B}(J)$ denote the le
Externí odkaz:
https://doaj.org/article/8ca12431b0f7483bb651f5cc246d10d9
A Furstenberg family $\mathcal{F}$ is a collection of infinite subsets of the set of positive integers such that if $A\subset B$ and $A\in \mathcal{F}$, then $B\in \mathcal{F}$. For a Furstenberg family $\mathcal{F}$, finitely many operators $T_1,...
Externí odkaz:
http://arxiv.org/abs/2205.10638
Autor:
Mohamed Amouch, Otmane Benchiheb
Publikováno v:
Boletim da Sociedade Paranaense de Matemática, Vol 42 (2024)
An operator $T$ acting on a Banach space $X$ is said to be recurrent if for each $U$; a nonempty open subset of $X$, there exists $n\in\mathbb{N}$ such that $T^n(U)\cap U\neq\emptyset.$ In the present work, we generalize this notion from a single ope
Externí odkaz:
https://doaj.org/article/df9ed73c597a40ef97fb6d3b64cebc11
Publikováno v:
Boletim da Sociedade Paranaense de Matemática, Vol 42 (2024)
In this paper we introduce and study the notions of hypercyclicity and transitivity for random dynamical systems and we establish the relation between them in a topological space. We also introduce the notions of mixing and weakly mixing for random d
Externí odkaz:
https://doaj.org/article/4a633c600a914038b5a2efbbda21d407
A bounded linear operator $T$ acting on a Hilbert space $\mathcal{H}$ is said to be recurrent if for every non-empty open subset $U\subset \mathcal{H}$ there is an integer $n$ such that $T^n (U)\cap U\neq\emptyset$. In this paper, we completely chara
Externí odkaz:
http://arxiv.org/abs/2108.01956
An operator $T$ acting on a Banach space $X$ is said to be super-recurrent if for each open subset $U$ of $X$, there exist $\lambda\in\mathbb{K}$ and $n\in \mathbb{N}$ such that $\lambda T^n(U)\cap U\neq\emptyset$. In this paper, we introduce and stu
Externí odkaz:
http://arxiv.org/abs/2108.01424
Autor:
Amouch, Mohamed, Benchiheb, Otmane
In this paper, we introduce and study the notion of super-recurrence of operators. We investigate some properties of this class of operators and show that it shares some characteristics with supercyclic and recurrent operators. In particular, we show
Externí odkaz:
http://arxiv.org/abs/2102.12170
Autor:
Amouch, Mohamed, Benchiheb, Otmane
Let $X$ be a complex topological vector space and $L(X)$ the set of all continuous linear operators on $X.$ In this paper, we extend the notion of the codiskcyclicity of a single operator $T\in L(X)$ to a set of operators $\Gamma\subset L(X).$ We pro
Externí odkaz:
http://arxiv.org/abs/2102.12174
Autor:
Amouch, Mohamed, Benchiheb, Otmane
An operator $T$ acting on a Banach space $X$ is said to be recurrent if for each $U$; a nonempty open subset of $X$, there exists $n\in\mathbb{N}$ such that $T^n(U)\cap U\neq\emptyset.$ In the present work, we generalize this notion from a single ope
Externí odkaz:
http://arxiv.org/abs/1907.05930