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Bishop's property (β), hypercyclicity and hyperinvariant subspaces [PDF]

Operators and Matrices, 2014
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Existence of hypercyclic subspaces for Toeplitz operators [PDF]

Ufimskii Matematicheskii Zhurnal, 2015
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IRREGULAR VECTORS AND SUBSPACE-HYPERCYCLIC OPERATORS

International Journal of Pure and Apllied Mathematics, 2013
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Frequently hypercyclic subspaces

Monatshefte für Mathematik, 2012
In [\textit{L. B. González} and \textit{A. Montes Rodríguez}, J. Approx. Theory 82, No. 3, 375--391 (1995; Zbl 0831.30024)], the authors started a new line of investigation by asking if an operator can possess an infinite-dimensional closed subspace all of whose non-zero vectors are hypercyclic, that is, vectors with a dense orbit.
Bonilla, A., Grosse-Erdmann, K.-G.
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On the existence of subspace-hypercyclic operators and a new criteria for subspace-hypercyclicity

Advances in Operator Theory, 2020
The notion of subspace-hypercyclicity was introduced by \textit{B. F. Madore} and \textit{R. A. Martínez-Avendaño} in [J. Math. Anal. Appl. 373, No. 2, 502--511 (2011; Zbl 1210.47023)]. A~bounded linear operator \( T \) on a Banach space \(X\) is called subspace-hypercyclic for a nonzero subspace \(M\) of \(X\), or simply, \(M\)-hypercyclic, if there ...
André Augusto, Leonardo Pellegrini
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Common Hypercyclic Subspaces

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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Semi-Fredholm Theory: Hypercyclic and Supercyclic Subspaces

Proceedings of the London Mathematical Society, 2000
The 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, León-Saavedra, Fernando, Montes-Rodríguez, Alfonso   +2 more
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Subspace-hypercyclicity of conditional weighted translations on locally compact groups

Positivity, 2022
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M. R. Azimi, M. Farmani
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Construction of dense maximal-dimensional hypercyclic subspaces for Rolewicz operators

Chaos, Solitons & Fractals, 2022
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Bernal-González, L., Calderón-Moreno, M. C., Fernández-Sánchez, J., Muñoz-Fernández, G. A., Seoane-Sepúlveda, J. B.   +4 more
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Hypercyclic subspaces of a Banach space

Integral Equations and Operator Theory, 2001
Let \(T\) 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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