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On linear chaos in function spaces

Jimenez John M., Markin Marat V.

Demonstratio Mathematica

2022

Vol. 55, nr 1

119--135

We show that, in Lp(0,∞) ( 1≤p<∞ ), bounded weighted translations as well as their unbounded counterparts are chaotic linear operators. We also extend the unbounded case to C0[0,∞) and describe the spectra of the weighted translations provided the underlying spaces are complex.

Mixing operators on spaces with weak topology

Shkarin S.

Demonstratio Mathematica

2011

Vol. 44, nr 1

143--150

We prove that a continuous linear operator T on a topological vector space X with weak topology is mixing if and only if the dual operator T′ has no finite dimensional invariant subspaces. This result implies the characterization of hypercyclic operators on the space ω due to Herzog and Lemmert and implies the result of Bayart and Matheron, who proved that for any hypercyclic operator T on ω, T⊕T is also hypercyclic.

A class of hypercyclic Volterra composition operators

Herzog G., Weber A.

Demonstratio Mathematica

2006

Vol. 39, nr 2

465-468

We prove that certain Volterra composition operators are hypercyclic on the Frechet space of all continuous functions u : [0,1) ->- R or C with u(0) = 0.