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The aim of the present paper is to investigate distributionally n-scrambled sets for weighted shift operators. We prove that the unilateral weighted shift operator admits densely invariant distributionally n-ε-scrambled linear… Click to show full abstract
The aim of the present paper is to investigate distributionally n-scrambled sets for weighted shift operators. We prove that the unilateral weighted shift operator admits densely invariant distributionally n-ε-scrambled linear manifolds for any ε ∈ (0, 1) and any integer n ⩾ 2, showing that this operator can exhibit maximal distributional n-chaos on a dense invariant linear manifold. Analogous results for the bilateral weighted shift operator are also obtained.
Keywords:
shift;
set weighted;
shift operators;
weighted shift;
scrambled set;
distributionally scrambled
Journal Title: Journal of Dynamical and Control Systems
Year Published: 2017
Link to full text (if available)
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Journal Title: Journal of Dynamical and Control Systems
Year Published: 2017
Link to full text (if available)
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recommendations!