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Distributional chaos for backward shifts |
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| Authors: | Fé lix Martí nez-Gimé nez |
| Affiliation: | a Departament de Matemàtica Aplicada and IUMPA, E.T.S.E. Agrònoms, Universitat Politècnica de València, E-46022 València, Spain b Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland c Departament de Matemàtica Aplicada and IUMPA, Edifici 7A, Universitat Politècnica de València, E-46022 València, Spain |
| Abstract: | We provide sufficient conditions which give uniform distributional chaos for backward shift operators. We also compare distributional chaos with other well-studied notions of chaos for linear operators, like Devaney chaos and hypercyclicity, and show that Devaney chaos implies uniform distributional chaos for weighted backward shifts, but there are examples of backward shifts which are uniformly distributionally chaotic and not hypercyclic. |
| Keywords: | Distributional chaos Hypercyclic operators Devaney chaos Backward shifts Kö the sequence spaces |
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