Results 91 to 100 of about 559 (116)
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Integral Equations and Operator Theory, 2005
We give a criterion for a family of operators to have a common hypercyclic subspace. We apply this criterion to a family of homotheties.
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We give a criterion for a family of operators to have a common hypercyclic subspace. We apply this criterion to a family of homotheties.
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Semi-Fredholm Theory: Hypercyclic and Supercyclic Subspaces
Proceedings of the London Mathematical Society, 2000The authors consider hereditarily hypercyclic operators \(T\) on Banach spaces \(B\), and give equivalent conditions for the existence of an infinite dimensional closed subspace \(B_1\) such that each \(z\in B_1\setminus \{0\}\) is an hypercyclic vector for \(T\). One condition, for example, is that the essential spectrum of \(T\) intersects the closed
González, Manuel +2 more
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Construction of dense maximal-dimensional hypercyclic subspaces for Rolewicz operators
Chaos, Solitons & Fractals, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bernal-González, L. +4 more
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Hypercyclic subspaces of a Banach space
Integral Equations and Operator Theory, 2001Let \(T\) be a bounded linear operator defined on a separable, infinite dimensional Banach space \(X\). If there is an \(x\in X\) for which \(\{T^nx\}_{n=0}^{\infty}\) is dense in \(X\), then \(x\) is a hypercyclic vector and \(T\) is a hypercyclic operator. An infinite dimensional, closed linear subspace, \(H \subseteq X\), is hypercyclic if every \(x\
Chan, Kit C., Taylor, Ronald D. jun
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A strictly weakly hypercyclic operator with a hypercyclic subspace
Journal of Operator TheoryAn interesting topic of study for a hypercyclic operator T:X→X on a topological vector space X has been whether X has an infinite\hyp{}dimensional, closed subspace consisting entirely, except for the zero vector, of hypercyclic vectors of T. These subspaces are called hypercyclic subspaces. It has been known that there is an operator T:H→H on a Hilbert
Chan, Kit C., Madarasz, Zeno
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Non-existence of frequently hypercyclic subspaces for P(D)
Israel Journal of Mathematics, 2016In this interesting article, the authors investigate whether the differential operators \(P(D)\), with \(P(z)\) a non-constant polynomial, have a frequently hypercyclic subspace on the Fréchet space \(H(\mathbb{C})\) of entire functions on the complex plane.
Bayart, Frédéric +2 more
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, 2023 Hypercyclicity and chaoticity spaces of $C_0$ semigroups
Discrete and Continuous Dynamical Systems, 2008Jacek Banasiak, Marcin Moszyński
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