Topological transitivity and mixing of composition operators
Let X=(X,B,μ) be a σ-finite measure space and f:X→X be a measurable transformation such that the composition operator Tf:φ↦φ∘f is a bounded linear operator acting on Lp(X,B,μ), 1≤p
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| Veröffentlicht in: | Journal of mathematical analysis and applications 2018-09, Vol.465 (1), p.125-139 |
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| container_end_page | 139 |
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| container_issue | 1 |
| container_start_page | 125 |
| container_title | Journal of mathematical analysis and applications |
| container_volume | 465 |
| creator | Bayart, Frédéric Darji, Udayan B. Pires, Benito |
| description | Let X=(X,B,μ) be a σ-finite measure space and f:X→X be a measurable transformation such that the composition operator Tf:φ↦φ∘f is a bounded linear operator acting on Lp(X,B,μ), 1≤p |
| doi_str_mv | 10.1016/j.jmaa.2018.04.063 |
| format | Article |
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We provide a necessary and sufficient condition on f for Tf to be topologically transitive or topologically mixing. We also characterize the topological dynamics of composition operators induced by weighted shifts, non-singular odometers and inner functions. 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We provide a necessary and sufficient condition on f for Tf to be topologically transitive or topologically mixing. We also characterize the topological dynamics of composition operators induced by weighted shifts, non-singular odometers and inner functions. 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| fulltext | fulltext |
| identifier | ISSN: 0022-247X |
| ispartof | Journal of mathematical analysis and applications, 2018-09, Vol.465 (1), p.125-139 |
| issn | 0022-247X 1096-0813 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_04605896v1 |
| source | ScienceDirect Journals (5 years ago - present); EZB-FREE-00999 freely available EZB journals |
| subjects | Composition operator Hypercyclic operator Linear chaos Linear dynamics Mathematics Topological dynamics |
| title | Topological transitivity and mixing of composition operators |
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