Supercyclicity of weighted composition operators on spaces of continuous functions
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Títol
Supercyclicity of weighted composition operators on spaces of continuous functionsData de publicació
2019-11-18Editor
SpringerISSN
2038-4815Cita bibliogràfica
Beltrán-Meneu, M.J., Jordá, E. & Murillo-Arcila, M. Supercyclicity of weighted composition operators on spaces of continuous functions. Collect. Math. (2019). https://doi.org/10.1007/s13348-019-00274-1Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
https://link.springer.com/article/10.1007/s13348-019-00274-1Versió
info:eu-repo/semantics/submittedVersionParaules clau / Matèries
Resum
Our study is focused on the dynamics of weighted composition operators defined on a locally convex space E ,→ (C(X), τp) with X being a topological Hausdorff space containing at least two different points and such ... [+]
Our study is focused on the dynamics of weighted composition operators defined on a locally convex space E ,→ (C(X), τp) with X being a topological Hausdorff space containing at least two different points and such that the evaluations {δx : x ∈ X}
are linearly independent in E0. We prove, when X is compact and E is a Banach space containing a nowhere vanishing function, that a weighted composition operator Cw,ϕ is never weakly supercyclic on E. We also prove that if the symbol ϕ
lies in the unit ball of A(D), then every weighted composition operator can never be τp-supercyclic neither on C(D) nor on the disc algebra A(D). Finally, we obtain Ansari-Bourdon type results and conditions on the spectrum for arbitrary weakly
supercyclic operators, and we provide necessary conditions for a composition operator to be weakly supercyclic on the space of holomorphic functions defined in non necessarily simply connected planar domains. As a consequence, we show that no
composition operator can be weakly supercyclic neither on the space of holomorphic functions on the punctured disc nor in the punctured plane. [-]
Publicat a
Collectanea Mathematica, 2019Proyecto de investigación
MEC: MTM2016-76647-P; MEC: MTM2016-75963-P; GVA/2018/110Drets d'accés
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