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Rotations of Hypercyclic and Supercyclic Operators
Integral Equations and Operator Theory, 2004A (bounded linear) operator \(T\) on a Banach space \(X\) is called hypercyclic if there is a vector \(x \in X\) such that its orbit \(\{T^n(x) \;| \;n=0,1,2,... \}\) is dense in \(X\); the vector \(x\) is called hypercyclic for \(T\). The operator \(T\) is called supercyclic if \(\{ \alpha T^n(x) \;| \alpha \in \mathbb C, n \in \mathbb N \}\) is dense
Fernando León-Saavedra +2 more
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Syndetically Hypercyclic Operators
Integral Equations and Operator Theory, 2005A sequence \((T_n)_{n\geq 0}\) of bounded operators on a separable \(\mathcal{F}\)-space \(X\) is hypercyclic if there exists a vector \(x\) in \(X\) such that the set \(\{T_n x \; ; \; n\geq 0\}\) is dense in \(X\). An operator \(T\) on \(X\) is hypercyclic if the sequence \((T^n)_{n\geq 0}\) of its powers is hypercyclic.
Peris, Alfredo, Saldivia, Luis
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Ideal of hypercyclic operators that factor through $\ell ^p$
, 2021We study the injective and surjective hull of operator ideals generated by hypercyclic backward weighted shifts that factor through $\ell^p$.
A. Aksoy, Y. Puig
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Multi-hypercyclic operators are hypercyclic
Mathematische Zeitschrift, 2001An operator \(T\) on a separable complex Hilbert space \(\mathcal H\) space is said to be hypercyclic if there is a vector \(x\) such that the orbit \(\{T^nx: n=0,1,\ldots\}\) is dense in \(\mathcal H\). An operator is said to be supercyclic if there is a vector \(x\) such that the scalar multiples of the elements in the orbit are dense in \(\mathcal H\
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Typicality of operators on Fréchet algebras admitting a hypercyclic algebra
Advances in Mathematics, 2023This paper is devoted to the study of typical properties (in the Baire Category sense) of certain classes of continuous linear operators acting on Fr\'echet algebras, endowed with the topology of pointwise convergence.
William Alexandre +2 more
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Weyl-type theorems for hypercyclic and supercyclic operators
Linear and multilinear algebraS-Weyl's theorem is a stronger variant of the classical Weyl's theorem for operators defined on Banach spaces. In this paper, we explore this variant in the case of hypercyclic or supercyclic operators on Banach spaces. Several applications are given for
P. Aiena +2 more
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Israel Journal of Mathematics, 2008
Let \(X\) be a complex infinite-dimensional separable Banach space and \(T\) be a bounded linear operator on \(X\). Let \(\Omega\) be a bounded domain of the complex plane whose boundary is a closed Jordan curve and \((F_n^{\Omega})_{n\geq 0}\) be the sequence of Faber polynomials of \(\Omega\).
Badea, Catalin, Grivaux, Sophie
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Let \(X\) be a complex infinite-dimensional separable Banach space and \(T\) be a bounded linear operator on \(X\). Let \(\Omega\) be a bounded domain of the complex plane whose boundary is a closed Jordan curve and \((F_n^{\Omega})_{n\geq 0}\) be the sequence of Faber polynomials of \(\Omega\).
Badea, Catalin, Grivaux, Sophie
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Residuality of Sets of Hypercyclic Operators
Integral Equations and Operator Theory, 2011Let \(X\) be a separable metrizable topological vector space and let \(L(X)\) denote the set of continuous and linear operators from \(X\) to \(X\). An operator \(T\in L(X)\) is called \textit{hypercyclic} if there exists a vector \(x\in X\) such that \(\{T^n x:n\in\mathbb{N}\}\) is dense in \(X\), and it is said to be \textit{supercyclic} if there ...
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Frequently Hypercyclic Composition Operators on The Little Lipschitz Space of A Rooted Tree
Mediterranean Journal of MathematicsWe characterize the strictly increasing symbols φ:N0⟶N0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength ...
Antoni L'opez-Mart'inez
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Cyclic and Hypercyclic Operators in Linear Dynamics
RESEARCH REVIEW International Journal of MultidisciplinaryLinear dynamics studies the orbit structure of continuous linear operators on infinite-dimensional topological vector spaces, bridging functional analysis with topological dynamics.
Anjeet Kumar
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