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$\epsilon$-hypercyclic operators that are not $\delta$-hypercyclic for $\delta$ < $\epsilon$

, 2023
For every fixed $\epsilon$ $\in$ (0, 1), we construct an operator on the separable Hilbert space which is $\delta$-hypercyclic for all $\delta$ $\in$ ($\epsilon$, 1) and which is not $\delta$-hypercyclic for all $\delta$ $\in$ (0, $\epsilon$).
openaire   +1 more source

ON THE HEREDITARILY HYPERCYCLIC OPERATORS

Journal of the Korean Mathematical Society, 2006
Bahman Yousefi, Ali Farrokhinia
openaire   +2 more sources

HYPERCYCLIC OPERATORS ON BANACH SPACES

Journal of Mathematical Extension, 2016
Panayappan Sethuraman
doaj  

Analytic hypercyclic operators

Matematychni Studii, 2008
Z. H. Mozhyrovska, A. V. Zagorodnyuk
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Disjoint hypercyclic operators [PDF]

Studia Mathematica, 2007
openaire   +1 more source

Numerically Hypercyclic Operators

Integral Equations and Operator Theory, 2012
Sung Guen Kim was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0009854). A. Peris was supported in part by MICINN and FEDER, Project MTM2010-14909, and by Generalitat Valenciana, Project PROMETEO/2008/101.
Alfred Peris
exaly   +5 more sources

Dual disjoint hypercyclic operators [PDF]

Journal of Mathematical Analysis and Applications, 2011
Let E be a separable Fréchet space. The operators T1,…,Tm are disjoint hypercyclic if there exists x∈E such that the orbit of (x,…,x) under (T1,…,Tm) is dense in E×⋯×E.
Héctor Nicolás Salas
exaly   +2 more sources

Hypercyclic operators failing the Hypercyclicity Criterion on classical Banach spaces

Journal of Functional Analysis, 2007
Let \(X\) be a topological vector space over \(\mathbb{R}\) or \(\mathbb{C}\). A (continuous, linear) operator \(T:X \to X\) is said to be hypercyclic if there exists some \(x \in X\) whose \(T\)-orbit \(\{T^n x: n\in{\mathbb{N}}\}\) is dense in \(X\). In [J.~Funct.~Anal.\ 99, 179--190 (1991; Zbl 0758.47016)], \textit{D.\,Herrero} posed the problem of ...
E Matheron
exaly   +3 more sources

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Rotations of Hypercyclic and Supercyclic Operators

Integral Equations and Operator Theory, 2004
A (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, Vladimir Müller   +1 more
exaly   +2 more sources