Abstract
In this paper, we introduce and study the diskcyclicity and disk transitivity of a set of operators. We establish a diskcyclicity criterion and give the relationship between this criterion and the diskcyclicity. As applications, we study the diskcyclicty of C0-semigroups and C-regularized groups. We show that a diskcyclic C0-semigroup exists on a complex topological vector space X if and only if dim(X) = 1 or dim(X) = ∞ and we prove that diskcyclicity and disk transitivity of C0-semigroups (resp C-regularized groups) are equivalent.
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The authors would like to thank warmly the referee for his suggestions and valuable comments on this paper.
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Amouch, M., Benchiheb, O. Diskcyclicity of Sets of Operators and Applications. Acta. Math. Sin.-English Ser. 36, 1203–1220 (2020). https://doi.org/10.1007/s10114-020-9307-3
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DOI: https://doi.org/10.1007/s10114-020-9307-3
Keywords
- Hypercyclicity
- supercyclicity
- diskcyclicity
- C0-semigroups of operators
- C-regularized groups of operators