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Pathological hypercyclic operators
Archiv der Mathematik, 2006We exhibit a hypercyclic operator whose square is not hypercyclic. Our operator is necessarily unbounded since a result of S. Ansari asserts that powers of a hypercyclic bounded operator are also hypercyclic. We also exhibit an unbounded Hilbert space operator whose non-zero vectors are hypercyclic.
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Frequently hypercyclic operators
2011The contents of this chapter are motivated by recent work on the application of ergodic theory to linear dynamics. While the technical difficulties involved prevent us from studying these tools here, we will discuss a new concept that has come out of these investigations, the frequently hypercyclic operators.
Karl-G. Grosse-Erdmann +1 more
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Hypercyclic Conjugate Operators
Integral Equations and Operator Theory, 2006We prove that for any weighted backward shift B = Bw on an infinite dimensional separable Hilbert space H whose weight sequence w = (wn) satisfies \( \sup_{n} {\left| {w_{1} w_{2} \ldots w_{n} } \right|} = \infty \), the conjugate operator \( C_{B} :S \mapsto BSB^{*} \) is hypercyclic on the space S(H) of self-adjoint operators on H provided with the ...
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Hypercyclic exponential of the differential operator on Banach spaces related to Fock spaces
Annals of Functional Analysis, 2023Ze-Hua Zhou
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Optimal growth of entire functions frequently hypercyclic for the differentiation operator
Journal of Functional Analysis, 2012Eero Saksman, David Drasin
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On S. Grivaux’ example of a hypercyclic rank one perturbation of a unitary operator
Archiv Der Mathematik, 2015Anton Baranov, Andrei Lishanskii
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On the set of hypercyclic vectors for the differentiation operator
Israel Journal of Mathematics, 2010Stanislav Shkarin
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The Density of the Hypercyclic Operators in the Strong Operator Topology
Integral Equations and Operator Theory, 2004Gabriel T Prajitura
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Hypercyclic subspaces for Fréchet space operators
Journal of Mathematical Analysis and Applications, 2006Henrik Petersson
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